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First Grade Math Worksheets

Free grade 1 math worksheets.

These printable 1st grade math worksheets help students master basic math skills .  The initial focus is on numbers and counting followed by arithmetic and concepts related to fractions, time, money, measurement and geometry.  Simple word problems review all these concepts.

Choose your grade 1 topic:

Number Charts & Counting

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Word Problems

Sample Grade 1 Math Worksheet

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Math Problems for Children 1st Grade

Welcome to the Math Salamanders Math Problems for Children 1st Grade. Here you will find our range of First Grade Math Word Problem Worksheets which will help your child apply and practice their Math skills to solve a range of problems.

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Math Problems for Children

Here you will find a range of problem solving worksheets.

The sheets involve using a range of math skills and knowledge to solve problems.

Each problem sheet is based around an interesting theme and comes complete with an answer sheet. The sheets are graded so that the easier sheets come first.

Using these sheets will help your child to:

• apply their addition and subtraction skills;
• apply their knowledge of place value;
• solve a range of problems.

1st Grade Math Word Problems

• At the Seaside 1

At the seaside 1 involves counting, as well as adding and subtracting small numbers. There are pictures to help children count on and back.

• PDF version
• Salamander Towers

Salamander Towers involves counting, working out small differences and comparing. There are pictures to support.

• Captain's Party

Captain's party involves adding and subtracting with small numbers without any pictures to support.

• The Bead Necklace

The Bead Necklace involves patterns and sequences, as well as counting, adding and reasoning.

• Salamander Fishing

This problem worksheet involves adding and subtracting numbers up to 20, and also ordering 2 digit numbers.

• Salamander Bowling

Salamander Bowling involves adding and subtracting numbers to 20, as well as ordering 2 digit numbers.

• At the Seaside 2

At the Seaside sheet 2 involves working out differences, adding and subtracting with numbers to 20.

Looking for some harder word problems?

If you are looking for some more challenging word problems, then try our 2nd Grade math word problems.

The problems are at a more challenging level and involve larger numbers.

• 2nd Grade Math Word Problems

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More 1st Grade Math Word Problems

Here you will find a range of math word problems aimed at first grade level. Each problem sheet is based on an interesting theme such as parties or the seaside.

Using these first grade math worksheets will help your child to:

• Add and subtract with numbers to 12;
• order numbers to 100;
• solve a range of math problems.
• 1st grade Addition Word Problems
• 1st Grade Subtraction Word Problems
• 1st Grade Addition and Subtraction Problems

Longer Math Problems

• First Grade Math Problems

First Grade Place Value and Counting Worksheets

Here you will find a range of 1st Grade Place Value Worksheets.

These first grade math worksheets will help your child learn their place value, reading, writing and ordering numbers up to 100.

There are also some money worksheets involving counting in dimes and pennies to support place value learning.

• learn to count in tens and ones;
• learn to order numbers to 100;
• learn to count in dimes and pennies;
• learn to read and write numbers to 100.

1st Grade Place Value Worksheets

• Math Place Value Worksheets Tens and Ones
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• 1st Grade Math Worksheets Counting by 1s and 10s

First Grade Math Games

Here you will find a range of free printable First Grade Math games. All children like to play Math games, and you will find a good range of 1st Grade Math Games here for your child to play and enjoy.

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All the free Math sheets in this section are informed by the Elementary Math Benchmarks for First Grade.

• 1st Grade Math Games

First Grade Math Puzzles

Here you will find a range of printable first grade math puzzles for your child to enjoy.

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Using these puzzles will help your child to:

• learn their addition facts to 12+12;
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• develop perseverance.
• Math Puzzles 1st Grade

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Home » 1st Grade Teaching Resources » 21 1st Grade Word Problems For Easy Math Skill Development

21 1st Grade Word Problems For Easy Math Skill Development

An important part of the curriculum, 1st grade word problems offer students an opportunity to apply the math concepts they have learned in class to everyday situations. 

Math class can be one of the most challenging subjects for children, so understanding and solving word problems about math in a practical way helps students practice math skills while applying different learning styles and understanding of math concepts in the real world. 

Table of Contents

Do 1st graders do word problems, best 1st grade word problem worksheets, how do you teach first grade word problems, about the author.

First grade students can do word problems by approaching them using what they already know: language skills like reading and listening, working together in teams, and manipulating objects to demonstrate and develop spatial sense. Word problems help students to understand the world around them, be able to solve real-world mathematical problems they can use in their everyday lives, and develop critical thinking skills, so it’s important to introduce word problems as early as 1st grade to help students think holistically about math.

In partnership with Teach Simple , whose marketplace is full of educational materials created by actual teachers (plus 50% of all revenues go to them), I have curated a list of 1st grade word problems on fantastic, interactive worksheets for teachers and parents to use to challenge students. They can be used in the classroom or at home . 

Children are often drawn to this kind of thinking, and there are lots of fun ways to make the experience playful and exciting for them. These worksheets and activities align with common core math standards for 1st grade, which include operations and algebraic thinking, numbers and operations, measurement and data, and geometry.  

Secret Word Problem Puzzles

These 5 sets of puzzles will help students add and subtract within word problems. Students solve the word puzzles and use their answers to figure out the code words. 

This bundle includes the secret code card, 8 word problems per set, response cards, and an answer key to check answers in 1 PDF file. 

Word Problems Solving Worksheet

With this worksheet, students can read the word problem and choose the correct operation to solve it. Simple yet effective, this printable sheet includes pictures and is available in 1 PDF file.  

Single Digit Addition Word Problem Activity

This printable worksheet has students solve single-digit addition word problems using colorful images and relatable situations. 

Math Strategy Cheat Sheet for Word Problems

This resource is a math strategy cheat sheet that students can utilize when solving word problems. When working on a problem, students can pull out this resource guide and determine which strategy will help them most. It includes 1 PDF with 2 ready-to-print pages.

Dental Math Word Problems Worksheet

This activity engages students by challenging them to solve word problems while learning all about the dentist! 

“ It’s Fall” Word Problems

These engaging math and literacy worksheet sets include word problems to be solved on a number line, as part-part-whole (number bonds), and in a drawing. This is an ebook download in PDF format.

Ocean Math Word Problems Activity

This activity engages students by asking them to solve word problems while learning about oceans. It contains 1 product file.  

Storytime Discoveries Math

The stories and activities in this book help make math fun through interesting folktales , poems, and original stories. Students learn about logical thinking, problem solving, and various mathematical concepts, such as measurement, shapes, telling time, addition, fractions, and map reading. 

”It’s Winter” Math Word Problems

When it’s cold outside, add some fun to your classroom with these engaging math problems. They have activities that can be used for morning work, homework, group work, or in learning centers. 

This product includes a word problem to be solved on a number line, as part-part-whole (number bonds), and in a drawing. 

Cut-and-Paste Math Word Problems

With this activity, students can practice word problems with cut-and-paste activities that provide hands-on practice for simple addition. Students read the problem, count out the amount they need, add them together, glue them onto their paper, then write their equation. 

2-Digit Addition, Subtraction, and Word Problems Workbook

This workbook provides practice for place value , two-digit addition and subtraction, odd and even numbers, and addition and subtraction word problems. It includes a 21-page printable packet with activities.

Frostyville Cinema Worksheets

These worksheets contain a variety of math skills that align with the curriculum. Students will work on reading a schedule and a menu, solving word problems, adding and subtracting money , and working on elapsed time. 

It has a fun wintertime theme and two different levels of problems, a color version, a black-and-white version, and the answer key.

Add and Subtract Word Problems Worksheet

This worksheet has add and subtract word problems ranging from 10 to 100.

10 Printable Word Problem Worksheets (Numbers 1–20)

This printable bundle has four word problems worksheets on addition, four on subtraction, and two worksheets on mixed operations.

Barnyard Math Word Problems

This activity engages students by asking them to solve word problems while learning about barnyard animals.

Harvest Theme Addition and Subtraction Word Problems

These materials are designed to be a follow-up activity after instruction on tens frame is presented. 

The word problems are presented on task cards. Students can answer the problems by using ten frames and apple-themed counters. Then, they can write their answers on a student recording sheet.

Math Word Problems Worksheet

These addition word problems include key words such as “in all,” “altogether,” “total number,” and “sum.” They have fun colorful pictures to make the problems interesting. These files are in a zipped folder with 8 sheets. 

First Grade Word Problems

This is a set of 30 math worksheets for first grade . They give students structured practice in solving addition and subtraction word problems, which involves both math and reading comprehension .

Addition Within 20 Word Problems Task Cards

These task cards each have an addition word problem with answers within 20. There are 20 cards, recording sheet, and answer key included.

Time Word Problems and Blank Clock Template

These printable worksheets are available in PDF format with 4 PDF worksheets with a blank template that includes analog clocks and empty boxes, to assist students practice giving varied times. Word problems are included in two worksheets for extra practice. Given certain time constraints, students must solve the problem and indicate when the event began and when it ends.

Multiplication for Primary Students

If you have any first graders that are ready to give multiplication a try, this resource contains 9 pages that will help your students understand multiplication.

The goal with 1st grade word problems is for students to develop skills like abstract and quantitative reasoning, applying mathematical tools they have already learned, and making sense of real-world mathematical scenarios. 

When teaching word problems to 1st grade students, we want to make sure we explain the problems clearly, note when students struggle with language comprehension (such as new vocabulary), and are available to provide support by talking out the problems with students. 

Here are some great tips for teaching word problems:

Tip 1: print them on good quality cardstock or laminate for durability and longevity, tip 2: print them on colored paper to engage students’, tip 3: remind students of different strategies they can use to solve word problems, tip 4: let students have access to the answer sheets once they have worked on the problem so they can self-correct, tip 5: have students work in groups, make the 1st grade word problems into a game, and get creative with your teaching style.

Jen Skolsky has a background in English, Psychology, and Creative Writing. She has taught for many years in international education, including ESL for all ages, middle school literature, speech and debate; high school AP Psychology, AP Language, AP Literature; university level Academic Writing, and Chinese Medicine Theory. She now works in marketing and book publishing.

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Free Printable Math Word Problems Worksheets for 1st Grade

Math Word Problems: Discover a collection of free printable worksheets for Grade 1 students, created by Quizizz, to enhance their problem-solving skills and mathematical understanding.

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Explore printable Math Word Problems worksheets for 1st Grade

Math Word Problems worksheets for Grade 1 are an essential tool for teachers to help their students develop strong foundational skills in mathematics. These worksheets provide a variety of engaging and challenging problems that cater to the unique learning needs of first-grade students. By incorporating these worksheets into their lesson plans, teachers can ensure that their students are exposed to a wide range of mathematical concepts, such as addition, subtraction, counting, and more. Furthermore, these worksheets are designed to be both fun and educational, keeping students interested and motivated to learn. With the help of Math Word Problems worksheets for Grade 1, teachers can effectively guide their students on the path to mathematical success.

Quizizz is an excellent platform that offers a variety of resources, including Math Word Problems worksheets for Grade 1, to support teachers in their quest to provide engaging and effective math instruction. In addition to worksheets, Quizizz also offers interactive quizzes, games, and other activities that can be easily integrated into lesson plans to create a dynamic and interactive learning environment. Teachers can utilize Quizizz's extensive library of resources to customize their lessons and address the specific needs of their students. By incorporating Quizizz into their teaching strategies, educators can ensure that their first-grade students receive a well-rounded and comprehensive math education that sets them up for success in future grades.

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Unit 2: Addition and subtraction

About this unit, relate addition and subtraction.

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Addition within 20

• Adding 7 + 6 (Opens a modal)
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Subtraction within 20

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Missing number within 20

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Word problems within 20

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Word problems with "more" and "fewer"

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Adding 1s and 10s

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Intro to addition with 2-digit numbers

• Adding 2-digit numbers without regrouping 1 (Opens a modal)
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• Breaking apart 2-digit addition problems (Opens a modal)
• Regrouping to add 1-digit number (Opens a modal)
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First Grade Math: Word Problems

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When first-grade students begin to learn math, teachers often use word problems and real-life examples to help students understand the complex language of mathematics. This establishes a foundation for higher education that the students will continue for at least the next 11 years.

By the time they finish the first grade, students are expected to know the basics of counting and number patterns, subtraction and addition, comparing and estimation, basic place values like tens and ones, data and graphs, fractions, two and three-dimensional shapes, and time and money logistics.

The following printable PDFs will help teachers better prepare students to grasp these core concepts for mathematics. Read on to learn more about how word problems help children to attain these goals before completing first grade.

Using Printable Worksheets as Teaching Tools

Deb Russell

Print the PDF: Word Problem Worksheet 1

This printable PDF provides a set of word problems that can test your student's knowledge of arithmetic problems. It also offers a handy number line on the bottom that students can use to help with their work!

How Word Problems Help First Graders Learn Math

Deb Russell 

Print the PDF: Word Problem Worksheet 2

Word problems like those found in this second printable PDF help students grasp the context surrounding why we need and use mathematics in everyday life, so it's essential that teachers ensure that their students understand this context and don't just arrive at an answer based on the math involved.

It breaks down to students understanding the practical application of math. If instead of asking students a question and a series of numbers that need to be solved, a teacher proposes a situation like "Sally has candy to share," students will understand the issue at hand is that she wants to divide them evenly and the solution provides a means to do that.

In this way, students can comprehend the implications of the math and the information they need to know to find the answer: how much candy does Sally have, how many people is she sharing with, and does she want to put any aside for later?

Developing these critical thinking skills as they relate to mathematics are essential for students to continue to study the subject in higher grades.

Shapes Matter, Too!

Print the PDF: Word Problem Worksheet 3

When teaching first-grade students early mathematics subjects with word problem worksheets, it's not just about presenting a situation in which a character has a few of an item and then loses some, it's also about ensuring students understand basic descriptors for shapes and times, measurements, and amounts of money.

In this linked worksheet, for instance, the first question asks students to identify the shape based on the following clues: "I have 4 sides all the same size and I have 4 corners. What am I?" The answer, a square, would only be understood if the student remembers that no other shape has four equal sides and four corners.

Similarly, the second question about time requires that the student be able to calculate addition of hours to a 12-hour system of measurement while question five asks the student to identify number patterns and types by asking about an odd number that's higher than six but lower than nine.

Each of the linked worksheets above covers the full course of mathematics comprehension required for completing the first grade, but it's important that teachers also check to ensure their students understand the context and concepts behind their answers to the questions before allowing them to move to second-grade mathematics.

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Check Out These 50 First-Grade Math Word Problems of the Day

Desmond saw 5 bunnies.

Opening your daily math lesson with a Math Word Problem of the Day is an excellent way to set the stage for learning. We all know that word problems are difficult for young learners to grasp, even when the mathematical operation portion of the problem is basic.

Incorporate these first grade math word problems one day at a time at the start of your math block to build confidence, critical thinking skills, and a learning community. Students will get used to reading slowly for meaning, while also identifying key information. Encourage students to write out equations and draw pictures to explain their thinking, since this helps them see the light when they are stuck!

Topics covered include addition, subtraction, multiplication, and comparison. All you need to do is post one of these first grade math word problems on your whiteboard or projector screen. Then let kids take it from there!

Want this entire set of word problems in one easy document? Get your free PowerPoint bundle by submitting your email here .

50 First Grade Math Word Problems

1. I had 6 pencils, and my teacher gave me 4 more. How many pencils do I have now?

2. Gina’s dog got 3 treats on Sunday and 0 treats on Monday. How many treats did Gina’s puppy get in all?

3. Joel went to the zoo with his family. During the first hour he was there he saw a bear, 2 tigers, and 3 lions. How many animals did Joel see in his first hour at the zoo?

4. Jackson sorted his toy cars by color. He has 6 blue cars, 5 green cars, and 4 black cars. How many cars does Jackson have in all?

5. Ben has 2 green balloons and 4 yellow balloons. How many balloons does he have altogether?

6. There are 3 kids in the Clark family. Tina is 3, Joshua is 4, and Samantha is 7. If you add up all their ages, what is the sum of the Clark kids?

7. If you go for a swim and 6 of your friends come along, how many friends are swimming in total?

8. Rachel’s mom had some flowers in a vase. 3 of the flowers wilted and Rachel’s mom took them out of the vase. Now there are 5 flowers in the vase. How many flowers were in the vase to start with?

9. Hayden’s cat had a litter of kittens. 3 kittens were gray, 2 kittens were spotted, and 7 kittens were black. How many kittens did Hayden’s cat have?

10. Pedro brought in 3 red leaves and 6 yellow leaves from the playground. How many leaves does he have in all?

11. Gabriella read 3 books on Monday, 6 books on Tuesday, and 4 books on Wednesday. How many books did Gabriella read in all?

12. If you have 3 cats, 2 guinea pigs, and a bunny. How many cute little noses do they have altogether?

13. If there are 3 inches of snow on the ground in the morning and we get 3 more inches of snow by dinner time. How many inches of snow did we get that day?

14. My cat has 4 paws and my brother’s dog has 4 paws. How many paws are there in all?

15. I had 10 pennies, but I lost 2 of them. How many pennies do I have now?

16. Santiago read 7 books over the summer. Ryan read 5 books. How many more books did Santiago read than Ryan?

17. Andrew put 10 stickers on his notebook. When he got to school he noticed some of the stickers had fallen off. Now Andrew only has 6 stickers on his notebook. How many stickers fell off Andrew’s notebook?

18. Nicole likes to help her mom pick tomatoes from their garden. She counted 9 tomatoes in the garden. 6 tomatoes were red and the rest were green. Nicole and her mom picked all the red tomatoes. How many green tomatoes did Nicole and her mom leave in the garden?

19. My sister and I have 20 pennies. If my sister has 10 pennies, how many pennies do I have?

20. The zoo had 8 tigers. 3 of the tigers moved to another zoo. How many tigers were left?

21. Esther read 3 poems. Magenna read some more poems. Altogether they read 7 poems. How many poems did Magenna read?

22. Haley’s dad bought 8 cheeseburgers. Haley ate 1 of them. How many cheeseburgers does Haley’s dad have left?

23. If you boil 7 eggs in water, and the number of eggs that float is one more than the number that sink, how many eggs float?

24. Rasheed loves to eat jellybeans. His favorite jellybeans are the yellow ones. There were 12 jellybeans in his bag. Rasheed removed all the yellow jellybeans and ate them, leaving 6 jellybeans in his bag. How many yellow jellybeans did Rasheed eat?

25. The gym teacher had 5 basketballs. The next week the gym teacher got some new basketballs. Now the gym teacher has 9 basketballs. How many new basketballs did the gym teacher get?

26. Jamal has 6 toy airplanes and his brother has 4 toy airplanes. How many more toy airplanes does Jamal have than his brother?

27. Antonio has some marbles. His brother Alex gives him 5 more. Now Antonio has 8 marbles. How many marbles did Antonio have to begin with?

28. If you have an 8-pack of crayons and you give your friend 3 of them to use during drawing time. How many crayons do you have in your pack now?

29. Emily has 4 pink erasers and some white erasers. She has 7 erasers in all. How many white erasers does Emily have?

30. Angel serves pizza at her birthday party. The pizza has 12 slices. 8 slices of pizza are eaten by Angel and her guests. How many slices of pizza are left?

31. If you have 9 toys on the floor and your little brother has 6 toys on the floor. How many more toys on the floor do you have?

32. There are 8 windows in the classroom. Some of the windows have decorations on them, 2 of them don’t have any directions. How many windows have decorations?

33. On Saturday, you brought home some fish from the pet store. If 15 of your 18 fish have stripes. How many of your fish are without strips?

34. 8 birds flew to the top of a fence. Some birds flew away and 6 birds stayed. How many birds flew away?

35. There were 6 books on Noah’s shelf. Olivia took some of the books. Now there are 2 books on the shelf. How many books did Olivia take?

36. Ethan has some folders in his backpack and 4 folders in his desk. He has 8 folders altogether. How many folders are in his backpack?

37. Liam has 8 t-shirts. 5 of them have superheroes on them, and the rest are solid colors. How many of Liam’s t-shirts are solid colors?

38. Mary was putting together a 20 piece puzzle. After she finished, she discovered that only 18 pieces were there. How many pieces were missing?

39. Nicholas has 7 cousins. Some of his cousins are girls and 3 of his cousins are boys. How many girl cousins does Nicholas have?

40. It snowed for 6 hours on Monday and 4 hours on Tuesday. How many more hours did it snow on Monday?

41. Charlie’s mom baked 12 chocolate chip cookies for dessert. Charlie ate 2 cookies and his mom and 1 cookie. How many chocolate cookies were left?

42. Melanie has 16 purple pens. Dante has 10 blue pens. Melanie has ____ more pens than Dante has.

43. Sofia has 75 pennies in her bank. How many more pennies will she need to have 100 pennies in her bank?

44. There were 9 cups of soda on the table. Some of the cups were knocked over, and 6 were still standing. How many cups of soda were knocked over?

45. Griffin has 20 board games. Some were under his bed, and 15 were in his closet. How many board games were under Griffin’s bed?

46. Antonio spotted 3 deer sitting at the top of a hill, but all he could see were their eyes. How many eyes did Antonio see in all?

47. Desmond saw 5 bunnies. He counted all of their ears. How many bunny ears did Desmond count?

48. Katie counted all of her toes, and then she counted all her mom’s toes. How many toes did Katie count altogether?

49. Which weighs more? A 15-pound red fox or a 24-pound wild turkey?

50. Which weighs more: a 150-pound white-tailed deer or a 110-pound kangaroo?

Enjoying these first grade math word problems? Check out our first grade hub for even more resources.

Get a PPT version of these word problems.

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Math Word Problem Worksheets for 1st Graders

First graders will get their first introduction to some very basic math word problems in these word problem worksheets. Each page has a few word problems along with some easy first grade problems to answer. If your students are having trouble solving addition and subtraction word problems, these worksheets will help get the practice they need.

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First Grade Math Problems – Story Problems

Welcome to the Breaking Down the Standards Series. Now that we have covered all things ADDITION & SUBTRACTION , this post will be a deep dive into first grade word problems. First grade problem solving will be one of the most challenging topics you’ll cover, so you’ll want to be aware of the Common Core / TEKs standards to help your students get the most out of your lessons.

1. First Grade Word Problems Standards:

To see the First Grade Problem Solving Standards for the Common Core and the TEKS, click the image above.

2. The Vertical Alignment for First Grade Problem Solving

Vertical Alignment for First Grade Word Problems is so important when planning your lessons. We need to examine not only the first grade standards, but also Kindergarten and 2nd grade standards as well. You need to know what your students should already know and also what they should know when their first grade year is over. Vertical alignment looks at the Kindergarten Standards as well as the Second Grade Standards and sets you and your students up for SUCCESS! Click the image above to see the Vertical Alignment.

Kindergarten: Can solve addition and subtraction word problems within 10 by using objects, drawings or number sentences to represent the problem.

1st Grade: Need to Learn: See #3 – The Breakdown

2nd Grade: (1.) Preparing to: Add/Subtract within 100, solve multi-step word problems within 1,000 using place value and algorithms. (2.) Generate problem situations when given an addition or subtraction number sentence of whole numbers within 1,000.

Need Second Grade Resources? Check these out from my friend Cynthia at My Kind of Teaching

3. The Breakdown: First Grade  Word Problems

When examining the standards to create the most productive and engaging lessons, keep your eye on the verbs . I’ve highlighted them in red. The verbs tell what your students will be doing to learn the standards.

When first graders leave first grade, they should be able to: (focus on the verbs in red)

• Solve Word Problems within 20 involving addition and subtraction with unknowns in all positions.
• Generate and S olve problems when given a number sentence involving addition and subtraction of numbers within 20.

First Grade Problem Solving Recommended Progression:

• Find the Sum (Friends of 10)
• Find the Sum (Within 10)
• Find the Sum (Within 20)
• Find the Missing Addend (Friends of 10)
• Find the Missing Addend (Within 10)
• Find the Missing Addend (Within 20)
• Find the Difference (Friends of 10)
• Find the Difference (Within 10)
• Find the Difference (Within 20)
• Comparing to find the Difference (How many more/fewer)
• Find the missing Subtrahend (Friends of 10) 10 – ___ = 6
• Find the Missing Subtrahend (Within 10) 9 – ___ = 5
• Find the Missing Subtrahend (Within 20) 16 – ___ – 10

Let’s Get Started

Word Problems   Manipulatives – The words “ Using  Objects “ is used over and over in the standards when the focus is on addition and subtraction. Make sure you have some kind of manipulatives for your student to use as they solve word problems. 

My Favorite Manipulatives: 

• Two Sided Counters
• Unifix Cubes
• Snap Cubes 
• 6 Colored Disks

2 Sided Counters, Snap Cubes and 6 Colored Counters are my favorites but use whatever you have.

Ahead of time, place 20 Snap Cubes or Two-Sided Counters in a baggie, ready to pass out to students. 

On a piece of chart paper, write out the following story problem. Leave room for pictorial model below.

Grace had 6 new pencils. Rex had 4 new pencils. How many new pencils did Grace and Rex have?  

Change the names to something familiar and meaningful to your students.

Read the chart altogether. Draw the pictures and create a number sentence to solve the problem. When complete, restate the question in the form of an answer.  

Example: Grace and Rex had 10 pencils altogether. This step should be done with each word problem. At this time, students should be asking themselves if the answer makes sense. This step should be done each time a child completes a word problem.

Mini Lesson Idea:

Use the progression from above and create a new chart with another word problem, getting progressively more difficult.

• Find the missing Subtrahend (Friends of 10)
• Find the Missing Subtrahend (Within 10)
• Find the Missing Subtrahend (Within 20)

First Grade Word Problem Discussion Points: Use these points each time you solve a word problem with your students.

• Read the problem altogether.
• Circle the important details that will assist with solving the problem.
• Underline or circle the question, so you can answer it later.
• Draw a pictorial model of what the word problem is saying. Use lines or dots for this.  You can also use blank ten frames. Otherwise, your math lesson will become a drawing exercise. Tell the students this and let them know that each line or dot represents the objects in the word problem.
• Ask the students if you will Add or Subtract. Then ask them how they know this.
• Solve the problem using addition or subtraction by creating a number sentence.
• Give the answer using a sentence that restates the question.
• Finally, ask if the answer makes sense.  

Word Problems Key Words

Some teachers like to expose their first grade students to Key Word for problem solving.  Sometimes this can cause difficulty if the student is unable to explain the “WHY” part.  Click the image below to grab the FREE Key Words Posters. As you come across these terms, ask your students what they think the terms mean. Then ask them WHY .

5.  First Grade Word Problems Practice

For your 1st graders to master the Common Core and TEKS Standards for problem solving , they will need practice for each step. This includes:

• Find the Sum
• Find the Difference
• Solve for the Missing Numbers in all Positions (Compare to find the Difference, Missing Addends & Subtrahends)

This can be done in a systematic way by using the editable template provided. Click the image below to grab the FREEBIE . To use it as a Google Slides resource, use as-is when you click the image. To use as a PowerPoint file, download the file from Google Drive and save it to your computer. You will most likely have to change the fonts to fit your needs.

6. First Grade Problem Solving Small Group Instruction: A Systematic Approach

Start with the least level of difficulty and move toward the greatest level of difficulty. This free resource has 12 1st Grade Word Problems that follow the progression above. It also includes an editable page so teachers can create their own word problem cards to use in their small group.  Click the image below to grab these FREEBIES

Grab the editable templates here.   To use that as a Google Slides resource, use as-is when you click the image. For PowerPoint: Download the PowerPoint file from Google Drive and edit in PowerPoint.

To keep practicing Basic Facts and the Related Skills, you might also like these:  

7. The Learning Centers: First Grade Word Problems

It’s time to practice first grade problem solving. There are so many ways to do this, ie. Learning Centers, Worksheets, Games… etc. So, I created this new resource that is fun and engaging! Introducing… Halloween Game Show (like Jeopardy) . Click on the image to check it out on TpT.

Here’s how Halloween Game Show works:

Students can be in teams, partners or may choose to work independently. They will choose a category and an amount, and a recording sheet is provided for them to keep track of their work. A Work it Out sheet is also provided for students to show their work. The students will work out the problem and check their answer. If they are correct, they gain points; and the team or person with the most points is the winner. There are 3 word problems for each category and each problem gets progressively harder. All are aligned to the standards and within 20.

Build a Monster – First Grade Problem Solving

Need a fun activity packet to keep your students busy for a while? Check out this  Build a Monster First Grade Word Problems Activity Packet ! Each time your student completes a story problems sheet (4 problems), they will color a piece of the monster. Once all 12 pages are complete, they can cut out the monster and put it together! Makes a great SUB PACKET!

Keep Practicing Addition & Subtraction 

As you work through the problem solving unit, you’ll want to keep practicing basic addition and subtraction facts. 

Here are some great resources for learning centers from my friend Carol (The Chocolate Teacher)  

8. The Fun: Spin a Story Problem for a Fun Learning Center

Your students can have fun while being creative as they spin a topic and use a ready made solution sentence to generate a story problem. This freebie comes with a generic spinner and the four seasons topics, plus 12 addition solution sentences and 12 subtraction sentences. It’s as easy as 1, 2, 3!  Grab a Solution Sentence, Spin the spinner and write the story problem. For example; let’s pretend that I grabbed 2 + 3 = 5 and I spun the jelly beans. Tim had 2 jelly beans. Saul gave Tim two more jelly beans. How many jelly beans does Tim have now? After creating the story problem, your student will either solve it on the recording sheet or allow a classmate to do so. Work continues until center time is up.

Click the image below to grab this freebie.

Add your name below to sign up for notifications of new posts from the Breaking Down the Standards Series AND Grab these Free First Grade Word Problems! 

Thank you for stopping by!

-Carrie Lutz

Disclosure: Carrie Lutz is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a small commission on products purchased through Amazon.com and other affiliated websites. You do not pay more when purchasing products through these links.

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Visual Models for Problem Solving in 1st Grade

May 10, 2020

As students enter 1st grade, they continue to work on math comprehension using early structures, like the Kindergarten journal we introduced last week, but now we begin to add visual models to the mix!

Let’s recap a child’s developmental journey through problem solving:

• In the early childhood years, a child needs lots of developmentally appropriate experience interacting with real objects in a physical world . 
• The physical world is captured in a quantitative picture , which young children observe and use as a springboard for mathematical conversations.
• We transition into a more structured math work mat to help young students be able to connect numbers to words and words to numbers, still using familiar situations from real life.
• The math work mat gives way to a formal math journal in Kindergarten that makes use of math comprehension skills. It provides a structure for students to explain their understanding of numbers within real world situations that will carry on throughout elementary school. 

Each of the stages of development builds on the skills developed in the previous step, so it is important that students aren’t rushed through these stages. The goal is to teach students the why behind the how so they aren’t just memorizing procedures but truly understand what is happening as they solve problems.

This 1st grade year is the last stage in the Math4Littles progression , in my opinion. After this, there isn’t much scaffolding, so we really want to carefully implement all the previous stages of problem solving before we turn the students loose, because we don’t want them to start guessing and checking. In taking students on this developmental journey, we are trying to build them a solid foundation for visual models to help them to understand problem solving. 

How We Used to Teach Problem Solving

When I was teaching 1st grade, I remember a strategy that we used for problem solving called the C.U.B.S. method. Each of those letters stood for a step in the problem solving process so students could remember what to do: C – circle the numbers, U – underline the word, B – box the operation, S – solve the problem. Seems like a simple process that gives kids a really great structure to start to understand what words problems are asking, right? But what I realized is that this strategy doesn’t hold up long term.

“Shannon has 5 lollipop and Scott has 4 more lollipops than Shannon. How many do they have all together?” 

I watched students follow that procedure with this type of problem. They circled the 4 and 5, underlined important information and put a box around the words all together , which means add because we’ve all seen the T-charts of addition/subtraction vocabulary – it says difference , it means we’re going to subtract, if you see all together , we’re going to add. But that strategy gives me 4, 5, and all together . If you go back to the question, you’ll realize the answer isn’t 9.

As I often do, I asked myself why ? Why isn’t it 9? A little more reading comprehension is required to decode that answer. The problem says I had 5 lollipops. Scott had 4 more than me, which means he also had 5. Adding that up, he had 9 and I had 5, so there were 14 all together.  

Why are we teaching kids procedures with concepts they don’t understand? Sometimes the strategies that we teach in math are conditional, meaning they only work for a certain amount of kids or a certain length of time. Then you have to worry about teaching them when to apply it and the rules for applying it, and what was meant to make things easier for students ends up being more complicated.

When we start working with strategies, I want to be able to find that vertical zip, meaning if I show you how this strategy might work in first grade, it has to work as the child gets older too so that they don’t have to learn a whole new set of strategies every year because every teacher teaches it differently. Honestly, the CUBS method would probably work for 75% of the problems in first grade. Students are doing more advanced part-whole addition problems, part-whole subtraction, part-whole missing addends, and they’ll start doing a few multi-step problems, all of which fit in the part-whole family, for which the CUBS method works well. But when you move out of that genre of problems, it falls apart. 

In the Kindergarten journal, we featured part-whole addition, part-whole subtraction, part-whole missing addend, a few problems with teen numbers, and a mixed review. The journal is very structured because it is intended to start students thinking about what they’re reading in the story problem: We have a story, a sentence form, a quick draw area, a number bond, a 10-frame, and a computation area. As they transition to 1st grade, how do we remove some of that scaffolding while still keeping it developmentally appropriate?

We have to be really careful with the way we make this transition, because very quickly, students can jump to the “circle the numbers, box the word” strategy and many times they just appeal to us because they don’t know what to do. It’s a word problem and it’s confusing, so they just add because we’re talking about adding that week. 

Additive Comparison Problems 

Additive comparison problems, where I have an amount and you have the same amount but you may have more or less than I do, are introduced after students have spent some time working on multi-step part-whole problems.

This type of problem is really a play on language, in my opinion, which makes it really confusing for kids to understand exactly what it is asking. So, we really want kids to take a step back to understand the additive comparison problems, which are coded AC in our journals. I find that building these problems with unfix cubes is a good way to start.

Let’s take this problem: Shannon has 10 pet rocks and Sherry has 4 pet rocks. How many more rocks does Shannon have than Sherry?

In some ways it seems like this might be a missing addend problem, but in fact we’re really comparing my pet rocks to Sherry’s pet rocks and we’re asking how many more does one have than the other. This really requires students to take it to the concrete level and make a bar model with unifix cubes.

I put 10 cubes to represent Shannon’s pet rocks, and then I’ll use different color cubes to show Sherry’s 4. Then, I want to compare the lengths of those two bars and figure out what the problem is really asking, which is the gap between where Sherry’s bar stops and Shannon’s bar stops. The question mark is asking for how many more does Shannon have? 

Sometimes, the language of an additive comparison problem might be reversed and say how many less does Sherry have? Since it is a play on words, which sometimes becomes confusing for students, we really need to put thought into how we go about teaching kids to do a problem like this.

Visual Models for Additive Comparison Problems

If I were to line up all the programs we work with, every one of them has bit of a different name for visual models: model drawings, tape diagrams, bar models, unit bars. We’re going to universally call them visual models for word problems. 

These aren’t the little quick draws we’ve been doing in Kindergarten because, as students get older and the problems get more complex, I’m not going to be able to draw 13 ducks and then 9 more because it will take too long! Instead, I want to put it into a visual model that has these units.

This first grade year is a transitional time where kids are going from the quick draw to what I’m going to call proportional bars, which have a length of individual cubes that are representative of the quantities we’re talking about in the problem.

I just was working with a first grade teacher last week on a Zoom call, and this teacher had not been able to attend our workshop on their campus about visual models. She, like most teachers I work with, didn’t understand why visual models were so important. She thought her students should be able to do quick draws and didn’t understand why they had to do boxes. She told me she was a big proponent of encouraging students to solve problems in different ways, so why would she possibly want to teach students a procedure like this and make them solve word problems in this way. 

After I took her through the same progression of problem solving we’ve been going through in our blog the past few weeks, she was sold! I took her up through fifth grade to help her see why it is that, in 1st grade, we’re asking students to stop doing quick draws and start to use a visual model that has a unit bar with different pieces. This proportional model is also a great transition into using a non-proportional bar.

Let’s say I had 92 pet rocks and Sherry has 45 pet rocks. A quick draw clearly won’t work for this problem, and I don’t have enough room on my paper to draw a proportional model for those numbers. But I can draw a longer bar that represents Shannon’s rocks, write in 92 rocks, and draw a shorter bar to show Sherry’s 45 rocks so I could see the proportionality. 

The hardest thing to remember when we do visual models for word problems is that it actually has nothing to do with math! We’re not actually solving the problem on the model; we are solely using a reading comprehension strategy.  

One of the biggest misconceptions we addressed when we started rolling out the 1st grade journal samples that I’ll be using in this video, was that the total doesn’t go on the line. If the problem asks for a total, we represent that in the visual model with a question mark. 

We also want to make sure that we label the visual model. For example, putting a B above the books that Erin had and an L above the books she got at the library. 

The whole point of this process is to provide a systematic way for students to work through problems that doesn’t stop working after 1st grade or when you start working on a different type of story problem. In fact, this strategy carries through multiplicative comparison problems and fractions, all the way into ratios and proportions in middle school. 

Step-by-Step Problem Solving

Read the problem. Then, have someone read it and repeat it, and every time a new piece of math information is presented, we’re going to put a chunk. So, as kids are reading the problem, they start to learn how to dissect what’s being asked. 

Not all first grade students will be able to read the story problem, but this process is modeled day after day after day in the first grade classroom, so eventually the child will become independent. 

I’m going to read a story problem: Mark has 9 strawberries, 6 of them are small. The rest are large. How many strawberries are large? 

Then, I’ll go back and read it in chunks: Mark has 9 strawberries . This is a new piece of mathematical information, so students will repeat that statement back and highlight or put a line there. The students also like to say chunk! Then we continue reading: Six of them were small. I’ll stop, repeat it, and the students say chunk! as they mark that chunk in their journals. Now we have two pieces of mathematical information. Let’s continue: The rest were large . Repeat and then chunk! So, we’ve got three sections of information that the problem has given us that we need to replicate in our visual model.  Finally, How many strawberries are large? Repeat that and then chunk!

By going through the problem slowly and methodically, students can really see these sections that they’re reading, and, as they’re going on to the subsequent steps of solving the problem, they can actually check off that they’ve included all the chunks of information in their visual model. 

In our problem, it asked me how many strawberries are large? To put it in a sentence form, I would say: Mark has ____ large strawberries. I like to say Hmm for the ____  as we’re reading it out loud.

In Kindergarten, we provide the sentence for students, leaving the blank space for their answer. But in 1st grade, we take some of the scaffolding away. It might say “There were _____ large ____” and the students have to fill in the blanks.

The sentence form is a great way to make sure that kids are comprehending what they’re reading. Generally, students in first grade have a difficult time trying to create a sentence form, because they aren’t yet developmentally ready to give you a complete answer in reading. But students will be required to do a sentence form in 2nd through 5th grade so we can be sure they understand the problems being asked, so it’s really great practice to start in 1st grade with the scaffolding.

Proportional model. We start the 1st grade year with a proportional model. We may scaffold here for the who or the what, and students will eventually start to learn what goes in that visual model. In this case, we’re talking about all of Mark’s strawberries, even though the question itself is only asking about how many of them are large.

In a proportional model, you might see the 9 squares. This is a missing addend problem so that title is going to have PWMA at the top, and there will be exactly nine squares. Some people might think that’s giving it away, but remember the goal of visual models? It’s not to solve the problem but understand what’s going on in the problem, so we’re more concerned about whether or not the student can label the drawing correctly. 

In this example, the student would total the bar at 9 and check off the first chunk of the problem that we read earlier –  Mark has nine strawberries.

The next part says “6 of them are small.” In 6 of my boxes, I’ll make six Xs, or I might make small circles, and at the top I can either write small or abbreviate with an s . 

Then it says “the rest are big.” I could label that other section of the boxes B for big, or write the whole word if I wanted. Then,  I need to put a question mark above that section between 9 (the total number of strawberries) and 6 (the number of small strawberries). That section represents the large strawberries, which is what my sentence form reminds me that I’m looking for. 

Technically, a student could just look at this easy proportional model and say there are 3 large strawberries because it’s right there in front of them. So some people might think this journal is just too easy, but at the end of the day, students are solidifying the process. They’re going back up to the problem and putting a check when they add Xs or circles for the six small strawberries. They’re putting in a check when they’ve talked about putting in the large strawberries. Then they put a question mark to show what we’re looking for. There’s a lot of detail that we’re looking for kids to have to interact with the text in math to show the comprehension. 

In some of our schools, we will do a unit bar at the bottom of the page. In the 1st grade journal we’ve created for Math4Littles, we’re going to leave the bar off and introduce the non-proportional bar a little bit later in the year. There is nothing wrong with having a model of the proportional bar and then underneath it having the non-proportional bar. In our journal, we plan to show the proportional bar, and then bring in both types of bars so that kids could see the relationship between the two. If where about this non proportional bar, where would I slice it to put the nine in? And then where’s my question mark? is it labeled? etc. 

The integral parts of visual models are: labelling the who or what, taking the bar and adjusting it based on the information that’s given, and writing in their question mark. Then it’s time to solve!

Computation. Although this step might not seem necessary because our sample problem is so simple, and to first graders after they do so many, it seems simple and both teachers and students might wonder why they’re even doing it, but I can promise that these problems will become more complex, very quickly. In our 1st grade journal, we will feature this look at the proportional bar, and then transition to having proportional and non proportional models, and then eventually just leaving it blank and having the student put in a non proportional bar to see that they can develop this progression. 

1st Grade Goals

The goal is, by the end of their first grade year, students should be able to solve problems with larger numbers and a non-proportional bar. You certainly don’t want to rush that progression. 1st grade is a really nice scaffold for students to get to that point of independence, because when we get to 2nd grade, we don’t do a whole lot of scaffolding. There are more open-ended sentences, more blanks, and students are doing more of the work.

Additionally, we want to mix up the types of problems we’re solving, give students time to understand them. You might do three days of part-whole addition to see if they can get it under their belt. Then do some part-whole subtraction, then mix the two to see if students are just following a pattern where we’re adding today or subtracting today. We want to know that they can really apply what they’re learning. Multi-step problems, where students have to add and then subtract, or vice versa, are next. Give students lots of good practice, and then mix it up again to see if they’re really following the words, or if they’re just learning a procedure. The last type of problem that we would integrate in the first grade is additive comparisons. 

Video Tutorials

In the video tutorials, you’ll see aspects of four different problems being displayed. Some will have the proportional bar, some will have the proportional and the non proportional and some just won’t have it just so you can get an overall idea of what this looks like as we go.

[yotuwp type=”playlist” id=”PL76vNL0J-a405ysBIwEwXfaMp5883yGh4″ ]

As you watch the videos, think about how you could set this up in your classroom, starting with some of the sample problems that we’re offering as a free download today. We will be releasing a full 1st grade journal soon, so stay tuned! 

Join us next week for problem solving in 2nd grade: What are the different problems that 2nd grade is going to encounter? How are journals coded?  As we start to look at how journals are coded, which you certainly could use these tutorial videos right away in your classroom or in your distance learning by thinking about story problems in a different way.

*Addition , *Subtraction , *Word Problems , Audience - Lower Elementary (K-2) , Series - Math4Littles | 0 comments

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Problem and Solution for First Grade

• Read Alouds , Reading & Literacy

Being able to easily identify the problem and solution in a story is a foundational reading comprehension skill for first grade students.

It's an activity that can be done with every single read aloud.

It can (and should) be done whole group, in small group, with partners, in literacy stations and during independent reading.

It's also a great skill for parents to work on at home. 

Describing the problem includes:

• Identifying the problem the character(s) is experiencing in the beginning of the story
• Asking questions and making predictions about possible upcoming events and about possible ways to solve the problem
• Understanding how the events and characters influence the problem throughout the story

Describing the solution includes: 

• Confirming or revising predictions about the resolution
• Explaining how the resolution solves the problem
• Describing what happens to the character(s) because of the resolution

Examples of Problem and Solution

You might be totally comfortable with the topic of problem and solution, but when we are in the moment in front of 22 little faces, sometime we blank! 

It's time to give our students examples of what Problem and Solution is…

but we've got nothing! 

It helps to think of a few examples ahead of time and jot them down. 

Examples of problem and solution work best if the are real life examples that the students can relate to! 

Here's a few examples from the school day: 

• Your pencil breaks
• You can't find your book
• You forgot your lunch
• You can't remember the directions
• You left your jacket on the playground
• You don't know how to tie your shoes
• You need a supply that another student is using

By using these real-life examples, you are not only teaching problem and solution, but you are reinforcing your classroom management as well!

How to Introduce Problem and Solution for First Grade

If you teach lower elementary, then you know that there is SO much that goes into the comprehension of a book. First grade students are learning so much at this age and even listening comprehension requires their little brains to work so hard.

Why do I bring this up?

Because I want you to think about how hard they are ALREADY working when they are listening to a read aloud and when you use a mentor text to introduce a NEW SKILL, most students’ brains go into overload!

So what should we do instead?

Start with a non-text activity. Let me introduce you to a new kind of “slideshow”. 

I like to use interactive slideshows/powerpoints. My slideshows always follow this order: 

• Teaching Slides: Introduces students to WHAT the skill is
• Guided Practice: Introduces students to HOW to apply the skill
• Interactive Practice: Gives students an example and allows them to PRACTICE the skill in an easy and concise way

Problem and Solution Non-Text Activities for First Grade

After we practice the slideshow, then we practice building our problem and solution muscles with some guided and independent practice using a NON-TEXT ACTIVITY such as a station game.

Non-text activities are a HUGE asset to students because it allows them to build and flex their problem and solution muscles before we ask them to apply those skills to a text! 

How to Complete the Activity

We will do this activity together as a group first, then it will move into our guided reading stations where students will complete it independently!

I've found the best and easiest way to do this is with images of problems/solutions that my first grade students know a lot about. 

My students do this Problem and Solution activity (seen on the right). We do one together as a class for guided practice. 

For this activity, students must correctly match the problem and solution. Then I have students write about the problem and solution with an emphasis on why the solution actually works for this problem.

After we do this activity together, it goes into their stations for Guided Reading. 

The best part about this activity is that you can leave it out for several weeks because each time students can choose a new set of pictures! 

Mentor Texts for Problem and Solution

A mentor text is an incredibly powerful tool for teaching reading comprehension skills! 

(make sure you keep reading to the end of this post to see a list of my favorite mentor texts for problem & solution)

The problem that many teachers run into with mentor texts is that there are SO MANY different skills you can teach with the same mentor text….

Sometimes we try to do TOO MUCH and we overwhelm our students! 

Let me introduce you to a Comprehension Focus Question (CFQ). 

A CFQ is one question that you focus on through the entire text! 

It simplifies things for you and your students. (more on that later)…

But let's take a minute to dispel so myths about mentor texts..

A mentor text is NOT a book that you read once and put it away.

A mentor text is a book that you read once, then refer back to again and again and again.

The greatest benefit of a good mentor text is that after you have read it once, when you refer back to it, you aren’t reading the entire book again, you are simply referring back to one or two pages.

It will save you SO much time.

AND students are already familiar with the story line meaning that already have a foundation for whatever comprehension skill you are about to dive into!

How to Boost Comprehension for Problem & Solution

Comprehension Focus Questions

As I mentioned, a Comprehension Focus Question (CFQ) is a very focused and intentional comprehension goal for an activity, a week or even a unit.

If you have done your research and you understand your learning standard, the vocabulary and what students need to know…

Then it becomes very easy to choose a goal (or a comprehension focus question).

But, why do you need a comprehension goal?

To stay FOCUSED!

Not just for you, but for your students also!

Let’s look at an example. Let’s say that this week you are focusing on how to make an inference. Well, there are about a hundred different ways you can make an inference and a CFQ allows you to focus on one area at a time.

Example CFQ: “How Did The Character Change From ___ To ____?”

In this comprehension focus question, you and your students are focusing in on the characters of the story.

The great thing about CFQ’s is that the next time you pull out this mentor text, you can choose a different CFQ to focus on while still practicing how to make an inference!

Sentence Stems

Another great strategy that falls right in long with mentor texts and comprehension focus questions is sentence stems.

A sentence stem is a phrase that your first grade students will use to answer a comprehension question.

Sentence stems are designed to get students to answer comprehension questions more fully rather than giving one word answers.

Sentence stems encourage students to explain their thinking.

I like to have a list of sentence stems next to my table that are specific to each comprehension skill. I stick to one or two stems per skill for the entire year because I want my students to be consistent. (This also makes it a lot easier for them)

If we are sticking with our Make an Inference example, I would use the following sentence stems:

I Think ___ Because____.   

I Read This ____ So I Think _____

Problem and Solution Activities for First Grade

All of the activities that you found in this post, both printable and digital, along with UNIT LESSON PLANS can be found in my Problem and Solution Bundle here.

You can save up to 20% by purchasing the items together, but you can also purchase individual items to better fit your needs!

Best Books for Problem and Solution

**You can use the recording sheet from the Problem and Solution station with all of these read alouds!

More First Grade Favorites

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Kristen Sullins

I am a current Elementary Librarian and Enrichment Teacher, mother of two, follower of Christ and Texas native. In my own classroom, I love to save time by finding unique ways to integrate writing, social studies and science into all parts of my day. I also love all things organization!

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enVision Mathematics - Middle School Math Curriculum

enVision® Mathematics offers a unique combination of problem-based learning and visual learning to develop conceptual understanding. This instructional model has been consistently successful and effective for middle school students across the nation.

• Motivate students through ownership of their learning with Let’s Investigate!
• Harness storytelling for instruction with engaging 3-Act Math problems
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Grades 6-8 Math Program Built for Success

Set students up for success in your class and beyond with a math curriculum that meets today’s challenges.

Student-Centered Mathematics

enVision ’s 3-Act Math, Let’s Investigate!, and Pick a Project components connect mathematical thinking to familiar real world scenarios so students stay engaged.

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Formative and summative assessments plus tools like MathXL® for School practice and enrichment and Savvy™ Adaptive Practice tailor assignments and content to each student’s interests and learning level.

Monitor and Support Student Understanding

Assess students’ progress, customize content, and reach or exceed state standard proficiency through the Savvas Realize® platform.

Comprehensive and Flexible Planning Materials

Editable lesson presentation slides allow teachers to present content and engage each student with customized content relevant to the students’ world around them.

Middle School Math Built for Students, Teacher, and Families

Unique and innovative lessons, motivating student projects.

• Enlightening Interactivities powered by Desmos™

Supportive Professional Development

Family engagement resources.

• Problem-Based Learning Real-world math problems foster collaboration skills. By evaluating options and presenting their own solutions, students stay engaged throughout the lesson.
• Productive Struggle Let’s Investigate! and 3 Act Math Modeling lessons allow students to experience productive struggle through inviting problem solving.
• Real-World Application Flexible student activities such as enVision STEM and Pick a Project provide opportunities for students to explore math concepts with real world application.

Enlightening Interactivities powered by Desmos™

• Concept Visualization Embedded interactivities throughout lessons help students visualize concepts
• Instructional Support and Insight Professional development videos, such as Using Manipultives videos, provide valuable instructional support and insight into student learning.
• Family-Friendly Support Every topic and lesson comes with family-friendly support that offers compatibility with Google Translate so that families can access resources in 300+ languages.

Award-Winning Digital Lesson Support

Savvas Realize® provides access to all the enVision Mathematics Grades 6-8 program’s digital resources and downloadable, editable print materials to meet every educational standard.

Offline Accessibility

Learning does not stop when students have no internet access. enVision ensures access to resources offline, automatically updating their work when reconnected!

Further Enhancements to the enVision 6-8 Math Program

• Meet Your Students Where They Are
• Personalized Programs
• Bilingual Support with enVision Mathématicas

Savvas Math Screener & Diagnostic Assessments

An easy and reliable way to identify student needs, assign the right content, and measure growth, delivered on Savvas Realize®.

SuccessMaker® Math helps learners at every level

This adaptive intervention program continuously personalizes math instruction for student growth or differentiation.

Embedded Spanish-Language Materials

Spanish texts, audio, and video come fully integrated within the Grade 6-8 courseware.

School Stories

In these inspirational stories, you'll learn about what schools and districts from across the country are doing to help students succeed and shape the future of education.

Frequently Asked Questions

enVision® Mathematics © 2024 for grades K-5 is the only middle grades math program that combines problem-based learning and visual learning to deepen students’ conceptual understanding. enVision is used by classrooms across the country and around the world. The latest enVision is even better with new digital Let’s Investigate! lessons which provide students with opportunities to take ownership of deeper exploration into problem-based learning. Ensure successful implementation with the comprehensive teacher support based on the 5 Practices.

enVision packs a unique one-two punch. Lessons start with Problem-Based Learning (PBL), where students must think critically about a real-world math problem, evaluate options, collaborate, and present solutions. This is followed by Visual Learning to solidify the underlying math concepts. It’s the best way to help kids better understand math ideas.

The program is made up of the following program components:

• Teacher’s Edition - Available in digital or print, the Teacher’s Edition includes wrap-around pages that provide direct instruction and teaching suggestions to engage students. The Interactive Teacher’s Edition online features annotation models and downloadable lesson resources.
• Student Edition - Interactive Student Edition—available in digital or print write-in format.
• enVision Digital - enVision digital courseware on Savvas Realize® includes robust digital tools that give teachers flexibility to use a digital, print, or blended format in their classrooms. Teachers can customize the program to rearrange content, upload their own content, add links to online media, and edit resources and assessments. All program resources, including personalized practice, remediation, and assessments are available in one location for easy lesson planning and presentation Students will use technology to interact with text and activities, and they can write directly in their digital Student Edition to make interaction with text more meaningful. Students will engage in activities that will inspire conceptual understanding, classroom discourse, and build their mathematical thinking skills, while learning to formulate and defend their own opinions.

The learning model in the enVision program—problem-based learning, visual learning, and data-driven differentiated instruction—has been researched and verified as effective. Core instruction used for every lesson has been shown to be effective for developing conceptual understanding.

enVision Mathematics features comprehensive differentiated instruction and intervention support to allow access for all students. The program’s balanced instructional model provides appropriate scaffolding, differentiation, intervention, and support for a broad range of learners, and is designed to facilitate conceptual understanding of mathematics for students at a range of learning levels.

Comprehensive, built-in differentiation resources support all levels of learners, including those with learning disabilities and ELLs, through personalized, adaptive learning. The program meets a variety of student needs and provides Response to Intervention (RtI) during each lesson, at the end of each lesson, at the end of each Topic, and any time as indicated in the Teacher’s Edition. A description of RtI tiered instructional resources for the program is included in the Teacher’s Program Overview for each grade. The following are examples of tiered instructional support found online for each lesson.

Tier 1 ongoing Intervention includes the following resources that can be used during the lesson:

• Prevent Misconceptions. During the Visual Learning Example, a remediation strategy is included to address a common misconception about the lesson concept.
• Error Intervention (If... Then...). During Practice & Problem Solving, error intervention identifies a common error and provides remediation strategy
• Reteaching Set. This set is provided before independent practice to develop understanding prior to practice.
• MathXL for School: Practice & Problem Solving, during the lesson, includes personalized practice for the Practice & Problem Solving portion of the lesson, along with Additional Practice or Enrichment; auto‐scored with on‐screen help, including Help Me Solve This and View an Example tools, tutorial videos, Math Tools, and one‐click animated glossary access.

Tier 2 strategic intervention includes the following resources that can be used at the end of the Lesson:

• Intervention Activity. This supports teachers working with small groups of struggling students.
• Reteach to Build Understanding. This provides guided reteaching as a follow‐up to the intervention activity.

Tier 3 intensive intervention instruction is delivered daily outside of the core math instruction, often in a one‐to‐one situation. The Math Diagnosis and Intervention System can be used for this purpose, for example.

• Variety of Instructional Strategies
• Multisensory instruction is provided in online Solve & Discuss It!/Explore It!/Explain It! activities that include audio, Visual Learning
• Animation Plus, Virtual Nerd videos, interactive MathXL for School: Practice & Problem Solving, Additional Practice, and Enrichment, online digital math tools, and online math games.

The authorship team is made up of respected educational experts and researchers whose experiences working with students and study of instructional best practices have positively influenced education. Contributing to enVision with a mind to the evolving role of the teacher and with insights on how students learn in a digital age, these authors bring new ideas, innovations, and strategies that transform teaching and learning in today’s competitive and interconnected world.

• Dr. Robert Q. Berry, III is an Associate Professor at the University of Virginia in the Curry School of Education with an appointment in Curriculum Instruction and Special Education. A former mathematics teacher, he teaches elementary and special education mathematics methods courses in the teacher education program at the University of Virginia. Additionally, he teaches a graduate level mathematics education course and courses for in-service teachers seeking a mathematics specialist endorsement.
• Zachary Champagne taught elementary school students in Jacksonville, Florida for 13 years. Currently he is working as an Assistant in Research at the Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCRSTEM) at Florida State University.
• Dr. Randall Charles is Professor Emeritus in the Department of Mathematics at San Jose State University, San Jose, California. His research interests have focused on problem solving with several NCTM publications including Teaching and Assessing Problem Solving, How to Evaluate Progress in Problem Solving, and Teaching Mathematics Through Problem Solving. In recent years Dr. Charles has written and talked extensively on Big Ideas and Essential Understandings related to curriculum, teaching, and assessment.
• Francis (Skip) Fennell, PhD, is emeritus as the L. Stanley Bowlsbey professor of education and Graduate and Professional Studies at McDaniel College in Maryland, where he continues to direct the Brookhill Institute of Mathematics supported Elementary Mathematics Specialists and Teacher Leaders Project. A mathematics educator who has experience as a classroom teacher, principal, and supervisor of instruction, he is a past president of the Association of Mathematics Teacher Educators (AMTE), the Research Council for Mathematics Learning (RCML), and the National Council of Teachers of Mathematics (NCTM).
• Eric Milou is a Professor in the Department of Mathematics at Rowan University in Glassboro, NJ. He is an author of Teaching Mathematics to Middle School Students. Recently, his focus has been on approaches to mathematical content and the use of technology in middle grades classrooms.
• Dr. Jane Schielack is Professor Emerita in the Department of Mathematics and a former Associate Dean of Assessment and PreK-12 Education in the College of Science at Texas A&M University. A former elementary teacher, Dr. Schielack has pursued her interests in working with teachers and students to enhance mathematics learning in the elementary and middle grades. She has focused her activities for improving mathematics education in two main areas: teacher education and professional development and curriculum development.
• Jonathan Wray has involvement and leadership in a number of organizations and projects. His interests include the leadership roles of mathematics coaches/specialists, access and equity in mathematics classrooms, the use of engaging and effective instructional models to deepen student understanding, and the strategic use of technology in mathematics to improve teaching and learning.
• How do I sign up for an enVision digital demo? enVision digital courseware on Savvas Realize® includes robust digital tools that give teachers flexibility to use a digital, print, or blended format in their classrooms. Teachers can customize the program to rearrange content, upload their own content, add links to online media, and edit resources and assessments. Program resources, personalized practice, remediation, and assessments are available in one location for easy lesson planning and presentation.

enVision Mathematics is designed to achieve a coherent progression of mathematical content within each course and across the program, building lesson to lesson. Every lesson includes online practice instructional examples as the progression of topics builds, allowing students additional practice with these skills and to develop a deeper conceptual understanding.

At the beginning of every topic, teachers are provided with support for the focus of the topic, how the topic fits into an overall coherence of the grade and across grades, the balance of rigor in the topic, and how the practices enrich the mathematics in the topic. Carefully designed learning progressions achieve coherence across grades:

Coherence is supported by common elements across grades, such as Thinking Habits questions for math practices and diagrams for representing quantities in a problem. Coherence across topics, clusters, and domains within a grade is the result of developing mathematics as a body of interconnected concepts and skills. Across lessons and standards, coherence is achieved when new content is taught as an extension of prior learning—developmentally and mathematically. (For example, Solve & Share at the start of lessons engages students in a problem-based learning experience that connects prior knowledge to new ideas.)

Look Back! and Look Ahead! connections are highlighted in the Coherence part of Topic Overview pages in the Teacher’s Edition.

The Topic Background: Rigor page shows teachers how the areas of rigor will be addressed in the topic, and details how conceptual understanding, procedural skill and fluency, and application builds within each topic to provide the rigor required.

On the first page of every lesson, the Lesson Overview includes sections titled Focus, Coherence, and Rigor. The Rigor section highlights the element or elements of rigor emphasized in the lesson, which may be one, two, or all three. Features in every lesson support each element, but the emphasis will vary depending on the standard being developed in the lesson. The core instructional model features support for conceptual understanding, procedural fluency, and application during both instruction and practice, as described below.

• Problem-Based Learning Step 1 Problem-Based Learning supports coherence by helping students connect what they already know to a problem in which new math ideas are embedded. When students make these connections, conceptual understanding emerges. Students are given time to struggle to make connections to the mathematical ideas and conceptual understandings. They can choose to represent their thinking and learning in a variety of ways. Physical and online manipulatives are available.
• Visual Learning Step 2 Visual Learning further develops understanding of the lesson ideas through classroom conversations. The Visual Learning Example features visual models to help give meaning to math language. Instruction is stepped out to help students visually organize important ideas. Students perform better on procedural skills when the procedures make sense to them. Procedural skills are developed through careful learning progressions in the Visual Learning Example.
• Assess and Differentiate Step 3 Assess and Differentiate features a Lesson Quiz and a comprehensive array of intervention, on-level, and advanced resources for all learners, with the goal that all students have the opportunity for extensive work in the state standards. Leveled practice with scaffolding is included at times. Varied problems are provided and math practices are identified as appropriate. Higher Order Thinking problems offer more challenge. Students have ample opportunity to focus on conceptual understanding and procedural skills and to apply the mathematics they just learned to solve a range of problems.
• How does the program identify performance gaps? At the start of the school year, schools have the opportunity to implement norm-referenced and validated assessments to identify students’ strengths and areas for growth. The new award-winning Math Screener and Diagnostic Assessments and Growth work directly with the enVision Mathematics course on Savvas Realize to inform instruction and provide robust student data. As a result of the Diagnostic assessment, teachers are armed with flexible instructional recommendations personalized to every student.

enVision Mathematics portrays diverse individuals and groups in a variety of settings and backgrounds. The program has been reviewed and approved for unbiased and fair representation. The selections in enVision Mathematics include a wide variety of contemporary, classic, and multicultural authors.

Our educational materials feature a fair and balanced representation of members of various cultural groups, including racial, ethnic, and religious groups; males and females; older people; and people with disabilities. The program integrates social diversity throughout all of its lessons, and includes a balanced representation of cultures and groups in multiple settings, occupations, careers, and lifestyles. We strive to accurately portray diverse groups within our society as well as diversity within groups. Our programs use language that is appropriate to and respectful of our cultural diversity. We involve members of diverse ethnic and cultural groups in the concept development of our products as well as in the writing, editing, illustration, and design.

• What is Pick a Project? Pick a Project is one of the motivating activities in enVision Mathematics , giving students a choice by letting them pick from a selection of math projects. Pick a Project launches each enVision topic and engages students in a real-world math project that accommodates different learning styles and interests. Students work independently, with a partner, or in small groups. The math problem activates prior knowledge and is a great way to deepen understanding during the entire topic.
• How does the relationship between enVision Mathematics and Desmos benefit students? Exclusive integration of Desmos into Savvas Realize® offers a groundbreaking interactive experience designed to foster conceptual understanding through highly visual interactives that bring mathematical concepts to life. Embedded interactives powered by Desmos and animated examples engage students and deepen conceptual understanding. Allowing students to manipulate data and see an immediate effect on graphs, number lines, etc. clarifies concepts as students are learning new content. Unique to enVision , the Desmos best-in-class graphing calculator and brand new geometry tools are available to middle and high school enVision students anytime, anywhere, both online and offline through Savvas Realize.

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How Students Can Rethink Problem Solving

Finding, shaping, and solving problems puts high school students in charge of their learning and bolsters critical-thinking skills.

As an educator for over 20 years, I’ve heard a lot about critical thinking , problem-solving , and inquiry and how they foster student engagement. However, I’ve also seen students draw a blank when they’re given a problem to solve. This happens when the problem is too vast for them to develop a solution or they don’t think the situation is problematic. 

As I’ve tried, failed, and tried again to engage my students in critical thinking, problem-solving, and inquiry, I’ve experienced greater engagement when I allow them to problem-find, problem-shape, and problem-solve. This shift in perspective has helped my students take direct ownership over their learning.

Encourage Students to Find the Problem 

When students ask a question that prompts their curiosity, it motivates them to seek out an answer. This answer often highlights a problem. 

For example, I gave my grade 11 students a list of topics to explore, and they signed up for a topic that they were interested in. From that, they had to develop a research question. This allowed them to narrow the topic down to what they were specifically curious about. 

Developing a research question initiated the research process. Students launched into reading information from reliable sources including Britannica , Newsela , and EBSCOhost . Through the reading process, they were able to access information so that they could attempt to find an answer to their question.

The nature of a good question is that there isn’t an “answer.” Instead, there are a variety of answers. This allowed students to feel safe in sharing their answers because they couldn’t be “wrong.” If they had reliable, peer-reviewed academic research to support their answer, they were “right.”

Shaping a Problem Makes Overcoming It More Feasible 

When students identify a problem, they’re compelled to do something about it; however, if the problem is too large, it can be overwhelming for them. When they’re overwhelmed, they might shut down and stop learning. For that reason, it’s important for them to shape the problem by taking on a piece they can handle.

To help guide students, provide a list of topics and allow them to choose one. In my experience, choosing their own topic prompts students’ curiosity—which drives them to persevere through a challenging task. Additionally, I have students maintain their scope at a school, regional, or national level. Keeping the focus away from an international scope allows them to filter down the number of results when they begin researching. Shaping the problem this way allowed students to address it in a manageable way.

Students Can Problem-Solve with Purpose

Once students identified a slice of a larger problem that they could manage, they started to read and think about it, collaborate together, and figure out how to solve it. To further support them in taking on a manageable piece of the problem, the parameters of the solution were that it had to be something they could implement immediately. For example, raising $3 million to build a shelter for those experiencing homelessness in the community isn’t something that students can do tomorrow. Focusing on a solution that could be implemented immediately made it easier for them to come up with viable options. 

With the problem shaped down to a manageable piece, students were better able to come up with a solution that would have a big impact. This problem-solving process also invites ingenuity and innovation because it allows teens to critically look at their day-to-day lives and experiences to consider what actions they could take to make a difference in the world. It prompts them to look at their world through a different lens.

When the conditions for inquiry are created by allowing students to problem-find, problem-shape and problem-solve, it allows students to do the following:

• Critically examine their world to identify problems that exist
• Feel empowered because they realize that they can be part of a solution
• Innovate by developing new solutions to old problems

Put it All Together to Promote Change

Here are two examples of what my grade 11 students came up with when tasked with examining the national news to problem-find, problem-shape, and problem-solve.

Topic: Indigenous Issues in Canada

Question: How are Indigenous peoples impacted by racism?

Problem-find: The continued racism against Indigenous peoples has led to the families of murdered women not attaining justice, Indigenous peoples not being able to gain employment, and Indigenous communities not being able to access basic necessities like healthcare and clean water.

Problem-shape: A lot of the issues that Indigenous peoples face require government intervention. What can high school teens do to combat these issues?

Problem-solve: Teens need to stop supporting professional sports teams that tokenize Indigenous peoples, and if they see a peer wearing something from such a sports team, we need to educate them about how the team’s logo perpetuates racism.

Topic: People With Disabilities in Canada

Question: What leads students with a hearing impairment to feel excluded?

Problem-find: Students with a hearing impairment struggle to engage with course texts like films and videos.

Problem-shape: A lot of the issues that students with a hearing impairment face in schools require teachers to take action. What can high school teens do to help their hearing-impaired peers feel included?

Problem-solve: When teens share a video on social media, they should turn the closed-captioning on, so that all students can consume the media being shared.

Once my students came up with solutions, they wanted to do something about it and use their voices to engage in global citizenship. This led them to create TikTok and Snapchat videos and Instagram posts that they shared and re-shared among their peer group. 

The learning that students engaged in led to their wanting to teach others—which allowed a greater number of students to learn. This whole process engendered conversations about our world and helped them realize that they aren’t powerless; they can do things to initiate change in areas that they’re interested in and passionate about. It allowed them to use their voices to educate others and promote change.