math problem solving examples for grade 7

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7th Grade Math Word Problems

Related Pages More Math Word Problems Algebra Word Problems More Singapore Math Word Problems 7th Grade Math Word Problems 2

In these lessons, we will look at some examples of 7th grade word problems with answers, solved using the Singapore Math block diagram method as well as using Algebra.

The following are some examples of 7th Grade Math Word Problems that deals with ratio and proportions.

These are Grade 7 word problems from a Singapore text. The problems are solved both using algebra (the way it is generally done in the US) and using block diagrams (the way it was shown in the Singapore text). You can then decide which one you prefer.

Singapore Math 2 (A Grade 7 Algebra Word Problem from a Singapore text)

Example: Mr. Rozario bought some apples and oranges. The ratio of the number of apples to the number of oranges are 2:5. He gave 3/4 of the apples to his sister and 34 oranges to his brother. The ratio of the number of apples to the number of oranges that he has now is 2:3. How many apples did Mr. Rozario buy? How many oranges did Mr. Rozario buy?

Example: At first, the ratio of Sam’s savings to Ray’s savings was 5:4. After each of them donated $45 to charity, the ratio of Sam’s savings to Ray’s savings became 13:10. What was Sam’s savings at first?

Example: Dan had 50% fewer stickers than Jeff. After Jeff gave 20 of his stickers to Dan, Dan had 40% fewer stickers than Jeff (had after he gave away 20 of his stickers). How many stickers did Dan have at first?

Example: There are 8 more girls than boys in a particular class. 3/5 of the boys and 1/3 of the girls were born in Georgia. If the number of boys that were born in Georgia is equal to the number of girls that were born in Georgia, how many students (boys and girls together) in that class were born in Georgia?

Example: Ray and Omar collect stamps. Originally, 1/5 of Omar’s stamps were equivalent to 1/3 of Ray’s stamps. If Ray gave Omar 24 stamps, Omar would have 3 times as many stamps as Ray. Find the number of stamps each of them had in the beginning.

Example: Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?

Example: The ratio of the amount of turkey to the amount of chicken at the grocery store was 8:3 in the morning. By the end of the day, 14 pounds of turkey had been sold. The ratio of the amount of turkey to the amount of chicken was now 3:2. a. How many pounds of turkey did the grocery store have in the morning? b. How many pounds of chicken did the grocery store have in the morning?

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Build Confidence with Math Problem Solving

Daily Problem Solving will help your 7th grade students master the skills they need to be successful with challenging word problems...and have fun doing it .

What you'll get with this download:

Your download includes a full week of Daily Problem Solving for Grade 7 to try out in your own classroom. Developed with the brain in mind, these multi-step word problems will challenge your learners without overwhelming them. Best of all, you'll be able to watch their skills and confidence grow as they begin to internalize strategies for conquering this difficult math skill.

FUN & ENGAGING

Themed-problems and a weekly fun fact make it easy to keep learners engaged

MINIMAL PREP

Formatted for quick & easy implementation that won't add stress to your planning

PRINT & DIGITAL

Includes both print and digital student options for added flexibility

I've been using this with my extremely anxious learner and it works wonders to build confidence because we see the improvement.

These have given me such an insight into my students' abilities, and I've watched them improve their skills and successfully solve multi-step word problems.

Jilliana D.

STUDENT PRINTABLES

You'll receive a full week of printable Daily Problem Solving practice for your students. This format includes:

• Paper-saving format that fits a full week on one page
• Space for student work, feedback, and self-reflection
• Themed problems & weekly fun fact to engage

DIGITAL SLIDES

Daily digital slides offer your remote or online learners the opportunity to build problem-solving skills in a structured format designed for success.

• Single slide per day prevents overwhelm or distraction
• Organized with clear space to solve & answer
• Engaging graphics, themed problems, & fun facts

Don’t wait, get started helping your learners master word problems today!

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Fractions and Mixed Numbers Grade 7 Math Questions and Problems With Solutions and Explanations

Detailed solutions and full explanations to fractions and mixed numbers grade 7 problems are presented.

• Find fraction F with denominator less than 8 such that 2 / 8 + F = 1 Solution Solve for F F = 1 - 2 / 8 = 8 / 8 - 2 / 8 , common denominator = 6 / 8 , subtract numerator = 3 / 4 , reduce fraction
• Find two fractions F1 and F2 with same denominator equal to 6 such that F1 + F2 = 1 and F1 - F2 = 2/3 Solution Let us write F1 + F2 and F1 - F2 as follows F1 + F2 = 1 = 6 / 6 F1 - F2 = 2 / 3 = 4 / 6 F1 and F2 are fractions with denominator 6. Their numerator must add up to 6 and their difference is 4. Hence F1 and F2 are equal to F1 = 5 / 6 and F2 = 1 / 6
• Which fraction is equivalent to 16%? Solution 16% is written as a fraction and reduced 16% = 16 / 100 = 4 / 25
• 1/2 + 1/5 + 1/6 = Solution The LCM of 2, 5 and 6 is first calculated 2 = 2 5 = 5 6 = 2 × 3 LCM = 2 × 5 × 3 = 30 We use the LCM as the lowest common denominator for all 3 fractions 1 / 2 + 1 / 5 + 1 / 6 = (1×15) / (2×15) + (1×6) / (5×6) + (1×5) / (6×5) Simplify = 15 / 30 + 6 / 30 + 5 / 30 Add and reduce = 26 / 30 = 13 / 15
• 3 3/5 + 5 1/2 = Solution Add whole parts together and fractional parts together 3 3/5 + 5 1/2 = (3 + 5) + (3/5 + 1/2) Common denominator for fractions 3/5 and 1/2 = 8 + (6/10 + 5/10) = 8 + 11/10 Change improper fraction 11/10 into mixed number and add = 8 + 10/10 + 1/10 = 8 + 1 + 1/10 = 9 1/10
• 1/7 × 2 2/5 = Solution Change the mixed number 2 2/5 into fraction and multiply 1/7 × 2 2/5 = 1/7 × 12/5 = 12 / 35
• 1/12 × 0.2 = Solution Change decimal number 0.2 into fraction 0.2 = 2/10 = 1/5 Multipliply the two fractions 1/12 × 0.2 = 1/12 × 1/5 = 1 / 60
• 2/5 ÷ 6 = . Solution Use division rule 2/5 ÷ 6 = 2/5 ÷ 6/1 = 2/5 × 1/6 = 2/30 Reduce fraction = 1/15
• 9/7 + 2 = . Solution Change 2 into fraction 2/1 and set common denominator. 9/7 + 2 = 9/7 + 2/1 = 9/7 + 14/7 = 23/7 = 3 2/7
• 2 1/3 + 4/2 = . Solution Simplify 4/2 and add. 2 1/3 + 4/2 = 2 1/3 + 2 = 4 1/3
• 3 1/5 ÷ 5 = Solution Change mixed number 3 1/5 into frcation and rewrite 5 as fraction 5/1. 3 1/5 ÷ 5 = 16/5 ÷ 5/1 = Apply rule of division of fractions and simplify. = 16/5 × 1/5 = 16/25
• 1/2 + 4 1/3 - 3 2/5 = Solution Add/subtract whole parts and fractional parts separately. 1/2 + 4 1/3 - 3 2/5 = 4 - 3 + 1/2 + 1/3 - 2/5 Find LCM of 2, 3 and 5 . 2 = 2 3 = 3 5 = 5 LCM(2,3,5) = 2×3×5 = 30 Use LCM as common denominator. = 1 + (15/30 + 10/30 - 12/30) = 1 + 13/30 = 1 13/30
• 5/2 ÷ 7/2 - 1/5 = Solution Order of operation division first 5 / 2 ÷ 7 / 2 - 1 / 5 = 5 / 2 × 2 / 7 - 1 / 5 Simplify = 5 / 7 - 1 / 5 Common denominator and subtract = 25 / 35 - 7 / 35 = 18 / 35
• (0.2 + 1/5) × 2/7 = Solution Change decimal number 0.2 into fraction 1/5 (0.2 + 1/5) × 2/7 = (1/5 + 1/5) × 2/7 Use order of opeartions = 2/5 × 2/7 = 4 / 35
• (3 1/2 + 3/5) × 1/7 = Solution Change mixed number 3 1/2 into fraction (3 1/2 + 3/5) × 1/7 = (7/2 + 3/5) × 1/7 Find common denominator to 7/2 and 3/5 and add = (35/10 + 6/10) × 1/7 = 41/10 × 1/7 Multiply fractions = 41 / 70
• (1/2 + 2/3) ÷ 0.2 = Solution Add the fractions within the brackets and write 0.2 as a fraction 1/5 (1/2 + 2/3) ÷ 0.2 = (3/6 + 4/6) ÷ 1/5 = 7/6 ÷ 1/5 Use rule of division of fractions = 7/6 × 5/1 = 35 / 6 = 5 5/6
• Order from least to greatest: 3 4/7 , 3 3/5 , 3 1/2 , 3 11/20 . Solution The given mixed numbers all have same whole parts but different fractions. It is easier to compare fractions when they have common denominator. The common denominator of the fractional parts is the LCM of 7,5,2,and 20. 7 = 7 5 = 5 2 = 2 20 = 2 2 × 5 LCM(7,5,2,20) = 7 × 5 × 2 2 = 140 We now rewrite all mixed with fractional parts with same denominator 3 4/7 = 3 80/140 3 3/5 = 3 84/140 3 1/2 = 3 70/140 3 11/20 = 3 77/140 We now order mixed numbers from least to greatest 3 1/2 , 3 11/20 , 3 4/7 , 3 3/5
• Order from least to greatest: 2 7/8 , 2.66 , 262% , 25/8 . Solution We need to rewrite the given numbers in a single form. Let us write them in decimal form 2 7/8 = 2 + 7/8 = 2 + 0.875 = 2.875 2.66 = 2.66 262% = 262 / 100 = 2.62 25/8 = 24/8 + 1/8 = 3 + 0.125 = 3.125 We now use the decimal form of the given numbers to order them from least to greatest. 262% , 2.66 , 2 7/8 , 25/8

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7th Grade Math Problems

In 7th grade math problems you will get all types of examples on different topics along with the solutions.

Keeping in mind the mental level of child in Grade 7, every efforts has been made to introduce new concepts in a simple language, so that the child understands them easily. The difficulty level of the problems has been reduced and mathematical concepts have been explained in the simplest possible way. Each topic contains a large number of examples to understand the applications of concepts. If student follow math-only-math they can improve their knowledge by practicing the solutions step by step which will help you to score in your exam.

●  Set Theory

Sets : An introduction to sets, methods for defining sets, element of set and use of set notations.

Objects Form a Set : State, whether the following objects form a set or not by giving reasons.

Elements of a Set : Learn how to find the elements of a set with the help of various types of problems on the basic concepts of sets.

Properties of Sets : Using the basic properties to represent a set learn to solve various basic types of problems on sets.

Representation of a Set : Definition with examples of statement form, roster form or tabular form, set builder form cardinal number of a set and the standard sets of numbers.

Different Notations in Sets : Some of the familiar notations used in sets which are generally required to solve various types of problems on sets.

Standard Sets of Numbers : Learn to represent the standard sets of numbers using the three methods i.e. statement form, roster form and set builder form.

Types of Sets : Definition with examples of empty set or null set, singleton set, finite set, infinite set, cardinal number of a set, equivalent set and equal sets.

Pairs of Sets : Definition with examples of equal set, equivalent set, disjoint sets and overlapping set.

Subset : Definition with examples of subset and its types, super set, proper subset, power set and universal set.

Subsets of a Given Set : How to find the number of subsets of a given set and number of proper subsets of a given set.

Operations on Sets : Learn the meaning. What are the four basic operations on sets? How the operations are carried out in union of sets and intersection of sets?

Union of Sets : Definition of union of sets with examples. Learn how to find the union of two sets and worked-out examples.

Intersection of Sets : Definition of intersection of sets with examples. Learn how to find the intersection of two sets and worked-out examples.

Difference of two Sets : Learn how to find the difference between the two sets and worked-out examples.

Complement of a Set : Definition of complement of a set and their properties with some worked-out examples.

Cardinal number of a set : Definition of a cardinal number of a set, the symbol used for showing the cardinal number, worked-out examples.

Cardinal Properties of Sets : Learn how to solve the real-life word problems on set using the cardinal properties.

Venn Diagrams : Learn to represent the basic concepts of sets using Venn-diagram in different situations.

● Relations and Mapping

Ordered Pair

Cartesian Product of Two Sets

Domain and Range of a Relation

Functions or Mapping

Domain Co-domain and Range of Function

● Relations and Mapping - Worksheets

Worksheet on Math Relation

Worksheet on Functions or Mapping

● Numbers - Integers

Multiplication of Integers

Properties of Multiplication of Integers

Examples on Multiplication of Integers

Division of Integers

Absolute Value of an Integer

Comparison of Integers

Properties of Division of Integers

Examples on Division of Integers

Fundamental Operation

Examples on Fundamental Operations

Uses of Brackets

Removal of Brackets

Examples on Simplification

● Numbers - Worksheets

Worksheet on Multiplication of Integers

Worksheet on Division of Integers

Worksheet on Fundamental Operation

Worksheet on Simplification

● Fractions

Types of Fractions

Equivalent Fractions

Like and Unlike Fractions

Conversion of Fractions

Fraction in Lowest Terms

Addition and Subtraction of Fractions

Multiplication of Fractions

Division of Fractions

● Fractions - Worksheets

Worksheet on Fractions

Worksheet on Multiplication of Fractions

Worksheet on Division of Fractions

● Story about the Decimal Number

Decimals : Concept for decimals in derails.

Decimal Numbers : Learn reading decimal numbers, writing decimal numbers etc,.

Decimal Fractions : Learn reading decimal fractions, writing decimal fractions.

Decimal Places : Learn reading and writing the place values of a decimal number in words.

Decimal and Fractional Expansion : Learn how to expand the decimal numbers and the decimal numbers in fractions

Like and Unlike Decimals : Learn to identify like decimals and unlike decimals.

Conversion of Unlike Decimals to Like Decimals : Learn to convert unlike decimals in like decimals

Comparing Decimals : Learn to order and compare decimal numbers, arranging decimals in ascending order and arranging decimals in descending order

Adding Decimals : Learn to add decimals in the correct order, word problems.

Subtracting Decimals : Learn to subtract decimals in the correct order, word problems

Simplify Decimals Involving Addition and Subtraction Decimals : Examples for simplifying decimals for adding and subtracting.

Multiplying Decimal by a Whole Number : Learn to multiply decimals by a whole number in the correct order, word problems

Multiplying Decimal by a Decimal Number : Learn to multiply decimals by a decimal number in the correct order, word problems

Dividing Decimal by a Whole Number : Learn to divide decimals by a whole number in the correct order, word problems

Dividing Decimal by a Decimal Number : Learn to divide decimals by a decimal number in the correct order, word problems

Simplification of Decimal : Examples for simplifying decimals, operation on decimals.

Converting Decimals to Fractions : Learn to express decimal number into fraction

Converting Fractions to Decimals : Learn to express fraction into decimal number

Rounding Decimals : Learn to round off decimals

Rounding Decimals to the Nearest Whole Number : Learn to round off decimals to the nearest whole number

Rounding Decimals to the Nearest Tenths : Learn to round off decimals to the nearest tenths

Rounding Decimals to the Nearest Hundredths : Learn to round off decimals to the nearest hundredths

Round a Decimal : Problems for rounding off decimals

H.C.F. and L.C.M. of Decimals : Learn to find the highest common factor, lowest common multiple of more than two decimal numbers

Terminating Decimal : Definition of terminating decimals, examples to identify terminating decimals

Non-Terminating Decimal : Definition of non-terminating decimal, examples to identify non-terminating decimals

Repeating or Recurring Decimal : Definition of recurring decimals, examples to identify recurring decimals

Pure Recurring Decimal : Definition of pure recurring decimal, examples to pure recurring decimal

Mixed Recurring Decimal : Definition of mixed recurring decimal, examples to identify mixed recurring decimal

Conversion of Pure Recurring Decimal into Vulgar Fraction : Learn to express pure recurring decimals to vulgar fractions with examples.

Conversion of Mixed Recurring Decimals into Vulgar Fractions : Learn to express mixed recurring decimals to vulgar fractions with examples.

BODMAS/PEMDAS rule:

BODMAS Rule : Learn how to follow the BODMAS rules to simply the order of operations.

BODMAS Rules - Involving Integers : Learn how to follow the BODMAS rules to simply the order of operations involving integers.

BODMAS/PEMDAS Rules - Involving Decimals : Learn how to follow the BODMAS rules to simply the order of operations involving decimals

PEMDAS Rule : Learn how to follow the PEMDAS rules to simply the order of operations.

PEMDAS Rules - Involving Integers : Learn how to follow the PEMDAS rules to simply the order of operations involving integers.

PEMDAS Rules - Involving Decimals : Learn how to follow the PEMDAS rules to simply the order of operations involving decimals.

● Profit, Loss and Discount

Concept of Profit and Loss

Calculate Profit and Profit Percent

Calculate Loss and Loss Percent

Calculate Cost Price using Sell Price and Loss Percent

Calculate Cost Price using Sell Price and Profit Percent

Calculate Selling Price using Cost and Loss Percent

Calculate Selling Price using Cost and Profit Percent

Calculating Profit Percent and Loss Percent

Word Problems on Profit and Loss

Examples on Calculating Profit or Loss

Practice Test on Profit and Loss

Practice Test on Profit Loss and Discount

● Profit, Loss and Discount - Worksheets

Worksheet to Find Profit and Loss

Worksheets on Profit and Loss Percentage

Worksheet on Gain and Loss Percentage

Worksheet on Discounts

● Ratios and Proportions

What is a Ratio?

What is a Proportion?

● Ratios and Proportions - Worksheets

Worksheet on Ratios

Worksheet on Proportions

● Time and Work

Calculate Time to Complete a Work

Calculate Work Done in a Given Time

Problems on Time required to Complete a Piece a Work

Problems on Work Done in a Given Period of Time

Problems on Time and Work

Pipes and Water Tank

Problems on Pipes and Water Tank

● Time and Work - Worksheets

Worksheet on Work Done in a Given Period of Time

Worksheet on Time Required to Complete a Piece of Work

Worksheet on Pipes and Water Tank

● Unitary Method

Problems Using Unitary Method

Situations of Direct Variation

Situations of Inverse Variation

Direct Variations Using Unitary Method

Direct Variations Using Method of Proportion

Inverse Variation Using Unitary Method

Inverse Variation Using Method of Proportion

Problems on Unitary Method using Direct Variation

Problems on Unitary Method Using Inverse Variation

Mixed Problems Using Unitary Method

● Unitary Method - Worksheets

Worksheet on Direct Variation using Unitary Method

Worksheet on Direct variation using Method of Proportion

Worksheet on Word Problems on Unitary Method

Worksheet on Inverse Variation Using Unitary Method

Worksheet on Inverse Variation Using Method of Proportion

● Simple Interest

What is Simple Interest?

Calculate Simple Interest

Practice Test on Simple Interest

● Simple Interest - Worksheets

Simple Interest Worksheet

● Algebraic Expressions

Division of Polynomial by Monomial

● Algebraic Expressions - Worksheets

Worksheet on Dividing Polynomial by Monomial

Formula and Framing the Formula

Change the Subject of a Formula

Changing the Subject in an Equation or Formula

Practice Test on Framing the Formula

● Formula - Worksheets

Worksheet on Framing the Formula

Worksheet on Changing the Subject of a Formula

Worksheet on Changing the Subject in an Equation or Formula

● Algebraic Identities

Square of The Sum of Two Binomials : Using the formula of (a + b) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + 2ab, learn to evaluate the square of the sum of two terms.

Square of The Difference of Two Binomials : Using the formula of (a - b)\(^{2}\)  = a \(^{2}\) + b \(^{2}\) - 2ab, learn to evaluate the square of the difference of two terms.

Product of Sum and Difference of Two Binomials : Using the formula of a \(^{2}\) - b \(^{2}\) = (a + b) (a - b), learn to evaluate the product of sum and difference of two terms.

Product of Two Binomials whose First Terms are Same and Second Terms are Different : Learn to use the given formulas to evaluate the product of the two terms whose 1 \(^{st}\) terms are same and 2 \(^{nd}\) terms are different.

• (x + a) (x + b) = x \(^{2}\) + x(a + b) + ab

• (x + a) (x - b) = x \(^{2}\) + x (a – b) – ab

• (x - a) (x - b) = x \(^{2}\) – x (a + b) + ab

• (x - a) (x + b) = x \(^{2}\) + x (b – a) – ab

Square of a Trinomial : Learn to use the formula for the expansion of the square of a trinomial.

• (a + b + c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) + 2ab + 2bc + 2ca

• (a + b - c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) + 2ab – 2bc - 2ca

• (a - b + c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) – 2ab – 2bc + 2ca

• (a - b - c) \(^{2}\) = a \(^{2}\) + b \(^{2}\) + c \(^{2}\) – 2ab + 2bc – 2ca

Cube of The Sum of Two Binomials : Learn the formula to determine the cube of the sum of two terms.

(a + b) \(^{3}\) = a \(^{3}\)   + 3a \(^{2}\) b + 3ab \(^{2}\)   + b \(^{3}\)

             = a \(^{3}\) + b \(^{3}\) + 3ab (a + b)

Cube of The Difference of Two Binomials : Learn the formula to determine the cube of the difference of two terms.

(a - b) \(^{3}\) = a \(^{3}\)   – 3a \(^{2}\) b + 3ab \(^{2}\)   – b \(^{3}\)

           = a \(^{3}\) – b \(^{3}\) – 3ab (a - b)

Cube of a Binomial :

Square of a Binomial :

● Equations

What is an Equation?

What is a Linear Equation?

How to Solve Linear Equations?

Solving Linear Equations

Problems on Linear Equations in One Variable

Word Problems on Linear Equations in One Variable

Practice Test on Linear Equations

Practice Test on Word Problems on Linear Equations

● Equations - Worksheets

Worksheet on Linear Equations

Worksheet on Word Problems on Linear Equation

● Inequations

What are Linear Inequality?

What are Linear Inequations?

Properties of Inequation or Inequalities

Representation of the Solution Set of an Inequation

Practice Test on Linear Inequation

● Inequations - Worksheets

Worksheet on Linear Inequations

● Lines and Angles

Fundamental Geometrical Concepts

Classification of Angles

Related Angles

Some Geometric Terms and Results

Complementary Angles

Supplementary Angles

Complementary and Supplementary Angles

Adjacent Angles

Linear Pair of Angles

Vertically Opposite Angles

Parallel Lines

Transversal Line

Parallel and Transversal Lines

● Congruence

Congruent Shapes :

Congruent Line-segments :

Congruent Angles :

Congruent Triangles :

Conditions for the Congruence of Triangles :

Side Side Side Congruence :

Side Angle Side Congruence : 

Angle Side Angle Congruence :

Angle Angle Side Congruence :

Right Angle Hypotenuse Side congruence :

Pythagorean Theorem :

Proof of Pythagorean Theorem :

Converse of Pythagorean Theorem :

Word problems on Pythagorean Theorem :

Polygon and its Classification

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Problems on Angle Sum Property of a Polygon

Sum of the Interior Angles of a Polygon

Sum of the Exterior Angles of a Polygon

● Polygons - Worksheets

Worksheet on Polygon and its Classification

Worksheet on Interior Angles of a Polygon

Worksheet on Exterior Angles of a Polygon

● Quadrilateral

Quadrilateral : Perimeter of Quadrilateral : Angle Sum Property of a Quadrilateral : Missing angle of a Quadrilateral :

Angles of a Quadrilateral are in Ratio :

●   Symmetrical Figure

Linear Symmetry :  Identify symmetric and non-symmetric figures and also identify shapes having horizontal line of symmetry, vertical line of symmetry, both horizontal and vertical lines of symmetry, infinite lines of symmetry and no line of symmetry.

Lines of Symmetry :  Identify the geometrical shapes having 1, 2, 3, 4, 0 and so on or infinite lines of symmetry.

Point Symmetry :  How to find the point symmetry of letters of the English alphabet and the different geometrical figures. Learn the important points to find the conditions that satisfy centre of symmetry.

Reflection Symmetry :

Reflection and Symmetry :

Nets of a Solids :

Rotational Symmetry :  Learn what is rotational symmetry and types of rotation i.e. clockwise rotation and anticlockwise rotation. 

Order of Rotational Symmetry :  Learn the different orders of rotation of the shapes through 360° in clockwise direction and anticlockwise direction.

Types of Symmetry :  Learn the various symmetries i.e. linear symmetry, point symmetry and rotational symmetry of the geometrical shapes. 

Reflection :  Learn how reflection is related to math, define reflection using an image and worked-out examples on math reflection. 

Reflection of a Point in x-axis :  Learn how to draw the image on the graph paper to find the reflection of a point in x-axis.

Reflection of a Point in y-axis :  Learn how to draw the image on the graph paper to find the reflection of a point in y-axis.

Reflection of a point in origin :  Learn how to draw the image on the graph paper to find the reflection of a point in origin. 

Rotation :  Explanation of rotation using an image.

90 Degree Clockwise Rotation :  Learn with the help of solved examples to rotate a figure 90 degrees clockwise direction around the origin on a graph paper.

90 Degree Anticlockwise Rotation :  Learn with the help of solved examples to rotate a figure 90 degrees anticlockwise direction around the origin on a graph paper.

180 Degree Rotation :  Learn with the help of solved examples to rotate a figure 180 degrees clockwise direction and anticlockwise direction around the origin on a graph paper.

●   Practical Geometry

• Practical Geometry
• Construction of a Circle

●  Coordinate System

• Coordinate Graph
• Ordered pair of a Coordinate System
• Plot Ordered Pairs
• Coordinates of a Point
• All Four Quadrants
• Signs of Coordinates
• Find the Coordinates of a Point
• Coordinates of a Point in a Plane
• Plot Points on Coordinate Graph
• Graph of Linear Equation
• Simultaneous Equations Graphically
• Graphs of Simple Function
• Graph of Perimeter vs. Length of the Side of a Square
• Graph of Area vs. Side of a Square
• Graph of Simple Interest vs. Number of Years
• Graph of Distance vs. Time

●  Mensuration

• Area and Perimeter
• Perimeter and Area of Rectangle
• Perimeter and Area of Square
• Area of the Path
• Area and Perimeter of the Triangle
• Area and Perimeter of the Parallelogram
• Area and Perimeter of Rhombus
• Area of Trapezium
• Circumference and Area of Circle
• Units of Area Conversion
• Practice Test on Area and Perimeter of Rectangle
• Practice Test on Area and Perimeter of Square

●  Mensuration - Worksheets

• Worksheet on Area and Perimeter of Rectangles
• Worksheet on Area and Perimeter of Squares
• Worksheet on Area of the Path
• Worksheet on Circumference and Area of Circle
• Worksheet on Area and Perimeter of Triangle

●   Volume and Surface Area of Solids

• Volume of Cubes and Cuboids
• Worked-out Problems on Volume of a Cuboid

●  Statistics

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Building Problem-solving Skills for 7th-Grade Math

Mathematics is a subject that requires problem-solving skills to excel. In 7th grade, students begin to encounter more complex math concepts, and the ability to analyze and solve problems becomes increasingly important. Building problem-solving skills for math not only helps students to master math concepts but also prepares them for success in higher-level math courses and in life beyond academics. 

In this article, we will several key skills that are needed for success in 7th-grade math, and also explore how they can benefit students both academically and personally. We will also provide tips and strategies to help students develop and improve their problem-solving skills. Let’s dive in!

Building Analytical Skills

The first of seven important skills to build is that of analytical skills. These allow students to analyze a problem and break it down into smaller parts. From there, they’re able to identify the key components that need to be addressed. Analytical skills also hone students’ abilities to identify patterns. Students should be able to identify patterns in mathematical data, such as in number sequences, geometric shapes, and graphs. Importantly, students should not just be able to recognize the pattens, but they should be able to describe them (more on that in communication) and use them to make predictions and solve problems.

We alluded to this earlier, but breaking down problems is an essential component of analytical skills. Students with strong analytical skills can break problems down into smaller and more manageable parts. They are then able to identify key components of a problem and use this information to develop a strategy for solving it. 

Along with identifying patterns comes identifying relationships. Students with good mathematical analytical skills can identify relationships between different mathematical concepts, such as the relationship between addition and subtraction, or the relationship between angles and shapes. Through strengthening this skill, students will be able to describe these relationships and use them to solve problems. 

An important part of analytical skills is the ability to analyze data. Students should be able to analyzeand interpret data presented in a variety of formats, such as graphs, charts, and tables. They should be able to use this data to make predictions, draw conclusions, and solve problems.

Speaking of conclusions, reaching sound conclusions based on mathematical data is a fundamental skill needed for making predictions based on trends in a graph, or drawing inferences from a set of data.

Another skill students should master is the ability to compare and contrast mathematical concepts, such as the properties of different shapes or the strategies for solving different types of problems. Through this, they’ll be able to use the information they gather to solve problems. 

With all these skills at play comes arguably the most important: Critical thinking. This is an indicator that a student really grasps the concepts and it’s just repeating them back to you on command. Critical thinking is the ability to evaluate information and arguments, and make judgements and decisions based on evidence, and apply logic and reasoning to solve problems.

Building Creative Thinking

This is the ability for students (or anyone, really) to think outside the box and come up with innovative solutions to problems. This involves being able to approach problems from different angles and to consider multiple perspectives. For a 7th-grader, this skill can be exercised through the following:

• Thinking Outside the Box: Students should be encouraged to think creatively and come up with innovative solutions to problems. This involves thinking outside the box and considering multiple perspectives.
• Finding Multiple Solutions: Students should be able to come up with multiple solutions to a problem and evaluate each one to determine which is the most effective.
• Developing Original Ideas: Students should be able to develop original ideas and approaches to solving problems. This involves being able to come up with unique and innovative solutions that may not have been tried before.
• Making Connections: Students should be able to make connections between different mathematical concepts and apply these connections to solve problems. This involves looking for similarities and differences between concepts and using this information to make new connections.
• Visualizing Solutions : Students should be able to visualize solutions to problems and use diagrams, charts, and other visual aids to help them solve problems.
• Using Metaphors and Analogies: Students should be able to use metaphors and analogies to help them understand complex mathematical concepts. This involves using familiar concepts to explain unfamiliar ones and making connections between different ideas.

Building Problem-Solving Strategies

It may sound like the same thing, but building problem-solving strategies is not the same as building problem-solving skills. Building strategies for problem-solving lends itself to actual problem-solving. Let’s expand on this: Say your student is presented a problem that they’re struggling with, these are some of the problem-solving strategies they may use in order to solve the puzzle.

• Identify the problem: The first step in problem-solving is to identify the problem and understand what is being asked. Students should carefully read the problem and make sure they understand the question before attempting to solve it.
• Draw a diagram: Students can draw a diagram to help visualize the problem and better understand the relationships between different parts of the problem.
• Use logic: Students can use logic to identify patterns and relationships in the problem. They can use this information to develop a plan to solve the problem.
• Break the problem down: Students can break a complex problem down into smaller, more manageable parts. They can then solve each part of the problem individually before combining the solutions to get the final answer.
• Guess and check: Students can guess and check different solutions to the problem until they find the correct answer. This method involves trying different solutions and evaluating the results until the correct answer is found.
• Use algebra: Algebraic equations can be used to solve a variety of mathematical problems. Students can use algebraic equations to represent the problem and solve for the unknown variable.
• Work backward: Students can work backward from the final answer to determine the steps required to solve the problem. This method involves starting with the end goal and working backward to determine the steps needed to get there.

Building Persistence and Perseverance

In an increasingly instant-gratification world with apps, searches and AI chatbots just a click away, this is an important skill not just in the math classroom, but for life in general. Problem-solving, whether that’s a math problem or a life challenge, often requires persistence and perseverance. Student need to learn to be able to stick with a problem even when it seems challenging, difficult, or seemingly impossible. Here are ways you can encourage your students to stick it out when working on problems:

• Trying multiple approaches: When faced with a challenging problem, students can demonstrate persistence by trying multiple approaches until they find one that works. They don’t give up after one attempt but keep trying until they find a solution.
• Reframing the problem: If a problem seems particularly difficult, students can demonstrate perseverance by reframing the problem in a different way. This can help them see the problem from a new perspective and come up with a different approach to solve it.
• Asking for help: Sometimes, even with persistence, a problem may still be difficult to solve. In these cases, students can demonstrate perseverance by asking for help from their teacher or classmates. This shows that they are willing to put in the effort to find a solution, even if it means seeking assistance.
• Learning from mistakes: Making mistakes is a natural part of the problem-solving process, but students can demonstrate persistence by learning from their mistakes and using them to improve their problem-solving skills. They don’t get discouraged by their mistakes, but instead, they use them as an opportunity to learn and grow.
• Staying focused: In order to solve complex math problems, it’s important for students to stay focused and avoid distractions. Students can demonstrate perseverance by staying focused on the problem at hand and not getting distracted by other things.

Building Communication Skills

We alluded to this earlier, but a central part of building problem-solving skills is building the ability to articulate a problem or a solution. This isn’t just for the sake of personal understanding, but critical for collaboration. Students need to be able to explain their thinking, ask questions, and work with others to solve problems. Here are some examples of communication skills that can be used to build problem-solving skills:

• Clarifying understanding: Students can ask questions to clarify their understanding of the problem. They can seek clarification from their teacher or classmates to ensure they are interpreting the problem correctly.
• Explaining their reasoning: When solving a math problem, students can explain their reasoning to show how they arrived at a particular solution. This can help others understand their thought process and can also help students identify errors in their own work.
• Collaborating with peers: Problem-solving can be a collaborative effort. Students can work together in groups to solve problems and communicate their ideas and solutions with each other. This can lead to a better understanding of the problem and can also help students learn from each other.
• Writing clear explanations: When presenting their solutions to a math problem, students can write clear and concise explanations that are easy to understand. This can help others follow their thought process and can also help them communicate their ideas more effectively.
• Using math vocabulary: Math has its own language and using math vocabulary correctly is essential for effective communication. Students can demonstrate their understanding of math concepts by using correct mathematical terms and symbols when explaining their solutions.

Building Mathematical Knowledge

This would seem like a no-brainer, since you’re a math educator clicking on an article about building math problem-solving skills. However, it’s worth being explicit that problem-solving in math requires a solid understanding of mathematical concepts, including arithmetic, algebra, geometry, and data analysis. Students need to be able to apply these concepts to solve problems in real-world contexts.

7th-grade math covers a wide range of mathematical concepts and skills. Here are some examples of mathematical knowledge that 7th-grade math students should have:

• Algebraic expressions and equations: Students should be able to write and simplify algebraic expressions and solve one-step and two-step equations.
• Proportional relationships: Students should be able to understand and apply proportional relationships, including identifying proportional relationships in tables, graphs, and equations.
• Geometry: Students should have a solid understanding of geometry concepts such as angles, triangles, quadrilaterals, circles, and transformations.
• Statistics and probability: Students should be able to analyze and interpret data using measures of central tendency and variability, and understand basic probability concepts.
• Rational numbers: Students should have a solid understanding of rational numbers, including ordering, adding, subtracting, multiplying, and dividing fractions and decimals.
• Integers: Students should be able to perform operations with integers, including adding, subtracting, multiplying, and dividing.
• Ratios and proportions: Students should be able to understand and use ratios and proportions in a variety of contexts, including scale drawings and maps.

In conclusion, problem-solving skills are essential for success in 7th grade math. Analytical skills, critical and creative thinking, problem-solving strategies, persistence, communication skills, and mathematical knowledge are all important components of effective problem-solving. By developing these skills, students can approach math problems with confidence and achieve their full potential.

If you enjoyed this read, be sure to browse more of our articles . More importantly, if you want to save yourself hours of preparation time by having full math curriculums, review guides and tests available at the click of a button, be sure to sign up to our 7th Grade Newsletter . You’ll receive loads of free lesson resources, tips and advice and exclusive subscription offers!

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SAMPLE MATH PROBLEMS FOR GRADE 7

Question 1 :

What is the square root of 196?

(A) 14                (B) 19                 (C) 12

Question 2 :

A play ground is 100 m long and 70 m wide. How much distance does a girl run when she runs 5 times around the playground?

(A) 2500 m      (B) 2300 m        (C) 1700 m

Question 3 :

From a rectangular sheet of tin, of size 100 cm by 80 cm, are cut four squares of side 10 cm from each corner. Find the area of the remaining sheet.

(A) 2400 cm 2       (B) 3600 cm 2         (C) 7600 cm 2

Question 4 :

If x = 2, y = 3 and z =-2 then find the value of  6x-7y + 4z

(A) 12                  (B) -17             (C) -10

Question 5 :

Find the value of x in 4 4x-7  = 4  x-1

(A) 2            (B) 5            (C) 3

Question 6 :

Expand (x  + 5y) 2

(A) x 2  + 10 xy + 25y 2      (B) x 2  - 10 xy - 25y 2   

(C) x 2  + 10 xy - 25y 2

Question 7 :

On selling a clock for $240, a trader loses 4%. In order to gain 10%, he must sell the clock for

(A) $275      (B) $295      (C) $365

Question 8 :

Find the remainder when 8x 3  - 12x 2  + 6x +15 divided by 2x-3. 

(A) 20         (B) 24         (C) 10

Question 9 :

The difference of two numbers is 72 and quotient obtained by dividing the one by other is 3. Find the numbers.

(A) 25, 97             (B) 15, 87          (C) 36, 108

Question 10 :

In triangle ABC, DE parallel to EC find AC when AB = 15 cm, AD  =  10 cm and AE  =  8 cm 

(A) 8 cm      (B) 4 cm      (C) 2 cm

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Problem Solving Activities: 7 Strategies

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Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

Shametria Routt Banks

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This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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Unit 1: Proportional relationships

About this unit.

Learn all about proportional relationships. How are they connected to ratios and rates? What do their graphs look like? What types of word problems can we solve with proportions?

Constant of proportionality

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Compare and interpret constants of proportionality

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• Interpreting graphs of proportional relationships Get 3 of 4 questions to level up!

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30 8th Grade Math Problems: Answers With Worked Examples

Erin Schumacher

8th Grade math problems build upon the basic algebraic reasoning and number system knowledge formed in prior grades. They help prepare students for more challenging math concepts that lay ahead of them in high school. 

In this blog, middle school math teacher, Erin, provides educators with 30 8th grade math problems to use in the classroom to strengthen learners’ math skills. Teachers can use these 8th grade math problems as warm-ups, competitive partner games, individual practice, or review before a test.

What are 8th grade math problems?

8th grade math problems are math problems specifically for 8th grade students focusing on the math skills and concepts learned in 8th grade. 

Many 8th grade math problems typically focus on algebraic reasoning to strengthen the foundations of solving for an unknown variable early on in the year. The majority of 8th grade math builds upon this skill. 

For example, when learning geometric concepts such as angle measures, surface area, volume, arc length, and sector area, formulas with an unknown variable are used to solve for measurement quantities.

Math Games For 8th Grade

15 fun math games and activities for 8th grade students to complete independently or with a partner.

8th grade math problems: Math curriculum

6th grade math problems and 7th grade math problems build the foundations for the 8th grade math curriculum. In 7th grade, students work with rational numbers and are introduced to simplifying algebraic expressions and solving algebraic equations. 

As students progress to 8th grade, a quick review of 7th grade material leads to a deeper dive into Algebra at a much faster pace.

The math curriculum in 8th grade hones in on linear functions and systems of equations where there are two variables rather than one. 

Perhaps, one of the biggest reasons 8th grade students struggle with the Common Core Math Standards is that they don’t have strong algebraic knowledge before introducing more than one variable.

30 8th grade math problems 

Here are 30 8th grade middle school math problems to help students practice and secure their knowledge of the core math concepts needed to succeed in high school and beyond. 

8th grade math problems: Rational number operations

Question 1 .

Add the values, then keep the negative sign when adding two negative numbers .

Question 2 

Answer:   -1\frac{11}{72} \text{ or } -\frac{83}{72}

This is another example of adding two negative numbers. Students must add the two fractions and then keep the negative sign.

Question 3 

Answer: \frac{53}{320}

Squaring a fraction means both the numerator and denominator are squared. Therefore: 

Show students how to enter fractions and exponents on their calculators. Calculators automatically reduce answers to the lowest terms and can help save students time.

READ MORE : What Is A Square Number?

8th grade math problems: Quotients of exponents, decimals, roots, and scientific notation

Question 4 .

Approximate the non-perfect root \sqrt{10} to the nearest tenth without using a calculator.

Answer: 3.2

The non-perfect root of 10 falls between the two perfect roots of 9 and 16.

Question 5 

Write the product of   \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} using the exponential form.

Answer: (\frac{2}{3})^{4}

Question 6 

Apply the Product of Powers Rule to simplify 4^{2} \times 4^{6} without using a calculator.

Answer: 4^{8}

The Produce of Powers Rule states that when the operation between to like bases raised to different powers is multiplication, keep the base and add the exponents.

8th grade math problems: Combining like terms and distributive property

Question 7 .

Answer: -4x-3

For struggling learners, circling one term and boxing the other works well. Additionally, using color to separate the terms is effective when several terms are used.

Answer: x+13

Explain to students that answers should often be reported with the variable listed before the constant.

Answer: -9x+27

Drawing arrows to visualize which terms are multiplied together can be very effective.

Teach students they can use negative signs and subtraction signs interchangeably in algebra. 

For example, 14-2 x means the 14 is positive and the 2 x is negative, even though the operation before the 2 x is a subtraction sign.

8th grade math problems: Solving one-step and two-step equations

Question 10 .

-4 + x = 10

Answer: x =14 

Visual aids and drawings of a vertical line through the equal sign improve some students’ understanding. This clearly indicates the “left” and “right” sides and the need to balance them. 

Other students do not like the vertical line, and I typically leave it off when showing my work.

Question 11

\frac{x}{120} =3

Answer: x= 360

Question 12 

Answer: x=\frac{1}{2}

8th grade math problems: Solving multi-step equations with the variable on both sides

Question 13 .

Answer: x = -6 

Question 14 

Answer: x= -4

Choose a side to move the x term to. I often told students to try and avoid working with negative numbers if they can, but it’s not necessary.

Question  15 

Answer: x = 44

When starting, it is helpful if all answers result in an integer. Students can then determine that something has gone wrong if they receive a fraction or decimal answer. 

For high-level learners, incorporate square roots of perfect squares and cube roots where applicable.

8th grade math problems: Special cases and determining the number of solutions

Question 16 .

Answer: All real numbers; infinite solutions

When the resulting statement is true (24=24) , any number can be used for x .

Question 17 

Answer: Undefined; no solution

When the resulting statement is false (-12=2) , this means no number can be used for x

Question 18 

-3(x+5)= -(3x+15) Answer: All real numbers; infinite solutions

Explain to students they should treat a negative sign (sometimes a subtraction sign) outside parentheses as a negative value that needs to be distributed.

8th grade math problems: Applying linear equations to word problems and real-world application

Question 19 .

Susie spent 2.75 hours on homework last night. She spent \frac{1}{4} hour longer on math than she did on reading. How much time did she spend studying both subjects?

Answer: Susie spent 1.25 hours reading and 1.5 hours on math.

Question 20 

In 5 years, Johnny will be twice as old as he is now. How old is Johnny now? Answer: Johnny is 5 years old.

Challenge students to read simpler word problems and write their own equations to represent the scenarios.

8th grade math problems: Linear functions

Question 21.

Is there a proportional relationship in this table of values? If so, find slope.  

Answer: Yes; slope = -1

The definition of slope is the change in y (dependent variable) divided by the change in x (independent variable).

Question 22

Graph the function y=3x+4

Have students use a t-chart to help identify coordinates before graphing. Later on, show students how to graph simply using the rules of y-intercepts and slopes.

Question 23

Write the equation of the line that passes through (1, -19) and (-2, -7)  in slope-intercept form.

Answer: y= -4x-15

8th grade math problems: Scatter plots

Question 24.

Give a possible scenario to relate the data in the graph provided.

Answer: There are many possible solutions to this question. Here is one possible answer: 

Question 25

Make a scatter plot from the data chart provided. Then, describe the correlation, if any.

The correlation shows a positive linear relationship between the x and y axis as both variables increase.

Question 26

Both graphs display the same data points. Write the equation of the trend line in the graph on the left, as it fits the data better than the trend line in the graph on the right.

Answer: y= -0.37x+7.46 

Extension: After students write the equation of the line of best fit on paper, challenge the students to plot the points on an online graphing calculator . 

Then, have students type y_{1} \sim mx_{1}+b  to see how close their equation matches the true linear regression.

8th grade math problems: Pythagorean Theorem, angles of triangles, surface area, volume

Question 27 .

Solve for the missing dimension in the right triangle.

Answer: x=8.1 \text{ feet} 

Question 28 

Calculate the measure of exterior angle A by solving for x . Use algebraic reasoning and apply the Exterior Angle Theorem.

Answer: A=108^{\circ}

Question  29

Calculate the surface area and volume for the given triangular prism .

Answer: \text{Surface area } = 68cm^2 ; \text{ Volume } = 30cm^3

Question 30 

Calculate the surface area and volume for the given cone. Round to the nearest hundredth.

Answer: \text{Surface area } = 75.40cm^2 ; \text{ Volume } = 37.70cm^3  

Top Tips for Teaching 8th Grade Math Problems

For success in teaching 8th grade math problems, educators should incorporate:  

• Rote skills
• Real-world application

Combining these teaching strategies is crucial for young learners. In my 15 years of experience as a math educator, students are more motivated to pay attention and power through lectures, note-taking, assignments, projects, and assessments if the educator figures out how to make the learning relevant and special to individuals. 

Simple things such as having students hand-write notes made a huge impact. Switching assignments between digital and paper frequently helped reduce groaning about the mundane. Incorporating art into math projects brought joy and opened students’ eyes to all the ways and places math is used in everyday life.

How can Third Space Learning help with 8th grade math?

STEM-specialist tutors help close learning gaps and address misconceptions for struggling 8th grade math students.

One-on-one online math tutoring sessions help students deepen their understanding of the 8th grade math curriculum and keep up with difficult math concepts before transitioning to high school.

Each student works with a private tutor who adapts instruction and math lesson content in real-time according to the student’s needs to accelerate learning.

8th grade math worksheets

Looking for more resources? Please see our selection of eighth grade math worksheets covering grade 8 key math topics and more:

• Solve Equations With Fractions Worksheet
• Adding and Subtracting Scientific Notation Worksheet
• Solving Inequalities Worksheet
• Ratios Problem Solving Worksheet
• Negative Exponents Worksheet

READ MORE :

• 2nd Grade Math Problems  
• Math Problems For 3rd Graders
• 4th Grade Math Problems
• Math Questions for 5th Graders
• Pythagorean theorem practice problems

Frequently asked questions

What math should an 8th grader know?

Upon completing the 8th grade, students should be well-prepared to enter Algebra 1. They should have a strong understanding of rational and irrational numbers, graphing, solving, and writing linear equations in standard form, slope-intercept form, point-slope form, inequalities, and functions including scatter plots, and geometry.

What grade is Algebra 1?

Algebra 1 typically starts in high school with 9th grade students.It is a high school math course that uses letters and mathematical symbols to solve math problems.

Do 8th grade students use a calculator?

8th grade students typically use calculators to help them solve most problems. Sometimes, an educator will ask students to think critically about an answer rather than relying on a device. However, many current educators understand that technology (including calculators) is readily available at any moment, and embrace using technology in everyday life.

Is 8th grade math hard?

8th grade math presents its challenges to many students. However, all students can succeed if using the tools accessible at their fingertips.

Do you have students who need extra support in math? Give your students more opportunities to consolidate learning and practice skills through personalized math tutoring with their own dedicated online math tutor. Each student receives differentiated instruction designed to close their individual learning gaps, and scaffolded learning ensures every student learns at the right pace. Lessons are aligned with your state’s standards and assessments, plus you’ll receive regular reports every step of the way. Personalized one-on-one math tutoring programs are available for: – 2nd grade tutoring – 3rd grade tutoring – 4th grade tutoring – 5th grade tutoring – 6th grade tutoring – 7th grade tutoring – 8th grade tutoring Why not learn more about how it works ?

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[FREE] Ultimate Math Vocabulary Lists (K-5)

An essential guide for your Kindergarten to Grade 5 students to develop their knowledge of important terminology in math.

Use as a prompt to get students started with new concepts, or hand it out in full and encourage use throughout the year.

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This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

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