7th class homework 2020

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Common Core - State Standards Initiative

• Students learn about ratios, mixed properties, statistics and other seventh grade skills.
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7th Grade Online Math Worksheets

According to the Common Core Standards, in Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples.

7th Grade Domains

If you know a particular Common Core Domain that you'd like to practice, you can drill down to it here.

• Analyze proportional relationships and use them to solve real-world and mathematical problems.
• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
• Draw, construct and describe geometrical figures and describe the relationships between them.
• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
• Use random sampling to draw inferences about a population.
• Draw informal comparative inferences about two populations.
• Investigate chance processes and develop, use, and evaluate probability models.

All 7th Grade Online Math Worksheets

This is a listing of all our 7th Grade Online Math Worksheets. Newest worksheets are on top!

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• Kindergarten
• Number charts
• Skip Counting
• Place Value
• Number Lines
• Subtraction
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• Word Problems
• Comparing Numbers
• Ordering Numbers
• Odd and Even
• Prime and Composite
• Roman Numerals
• Ordinal Numbers
• In and Out Boxes
• Number System Conversions
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• Size Comparison
• Measuring Length
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• Customary Unit Conversion
• Temperature
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• Writing Checks
• Profit and Loss
• Simple Interest
• Compound Interest
• Tally Marks
• Mean, Median, Mode, Range
• Mean Absolute Deviation
• Stem-and-leaf Plot
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• Permutation and Combination
• Probability
• Venn Diagram
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• Shapes - 2D
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• Lines, Rays and Line Segments
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• Transformation
• Quadrilateral
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• Midpoint Formula
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• Parallel, Perpendicular and Intersecting Lines
• Scale Factor
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• Pythagorean Theorem
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• Converting between Fractions and Decimals
• Significant Figures
• Convert between Fractions, Decimals, and Percents
• Proportions
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7th Grade Math Worksheets

Ease into key concepts with our printable 7th grade math worksheets that are equipped with boundless learning to extend your understanding of ratios and proportions, order of operations, rational numbers, and help you in solving expressions and linear equations, in describing geometrical figures, calculating the area, volume and surface area, finding the pairs of angles, and getting an insight into statistics and probability and much more! Instantly evaluate with our answer keys. Give our free grade 7 math worksheets a try and head over for more!

Select Grade 7 Math Worksheets by Topic

Explore 3,600+ Seventh Grade Math Worksheets

Writing the Equivalent Ratios

Create equivalent ratios that express the same relationship by multiplying the first and second term of the ratio by the same number. Also, complete the table with equivalent ratios.

• Download the set

Adding Integers Using Number Lines

Open doors to adding integers with our grade 7 math worksheet pdfs. Students start with the first addend, draw as many hops as the other addend toward the right or left on the number line, and find the sum.

Exponents and Operations

Take your skills in applying the order of operations up a notch as you evaluate the expressions involving fractions with positive and negative exponents.

Solving for 'x' | Side Lengths of Rectangles

With this set of printable 7th grade math worksheets, your students are well-equipped to practice setting up an equation with the indicated lengths, rearranging the equation, making 'x' the subject, and solving.

Enlarging or Reducing Shapes Using the Scale Factor

Find the dimensions of the figures on the grid, sketch the shapes on the grid, enlarging or reducing the original shape as instructed, multiplying the dimensions with the given scale factor.

Finding the Area of a Circle Using the Radius

Prepare students in grade 7 in finding the area of a circle using this printable collection of worksheets offering oodles of practice. Plug in the radius in the formula A = π * r 2 to find the area of the circle.

Area of Rectangles | Unit conversion

Make the units in the dimensions uniform by converting them to the units specified in the answer, multiply the length and width, and calculate the area of each rectangle.

Surface Area of Rectangular Prisms | Unit Squares

Finding the surface area doesn't feel like a chore with our 7th grade math worksheet pdfs. Count the number of unit squares on each of the six faces of the rectangular prism, multiply by the scale and add.

Finding Complementary Angles

Two angles are complementary if they add up to 90°. Subtract the angle from 90° to find its complement, state whether each given angle pair is complementary and find the measure of the unknown angle.

Comparing Mean Absolute Deviations

Perfect for calculating the mean absolute deviation or MAD of the two data sets using the formula, ∑|x i - x̅|/n, and comparing them, these printable math worksheets are a must-have for your grade 7 learners.

Forming a Proportion

A proportion is nothing but two ratios equivalent to each other. Form a proportion by identifying the four numbers that can be set up as a pair of equivalent ratios from the given set of 5.

Adding Integers

Rich with scads of practice, this set of math worksheet pdfs for 7th grade learners helps them add two integers with the same sign and subtract those with different signs, and figure out the sum instantly.

Squaring Numbers | Fractions

Multiply the given fraction by the same fraction to obtain its square. Convert the product to mixed numbers if required, and also identify the square of the given fraction from a pool of options.

Finding Side Lengths of Triangles Using the Perimeter

Our printable grade 7 math worksheets are an add-on to your practice in computing the side lengths of a triangle by equating the sum of linear expressions with the given perimeter, and solving for x.

Scale Factor | Perimeter and Area of Similar Figures

Upgrade your skills in calculating the area or perimeter of the original or dilated image using the scale factor and comprehend the impact of the scale factor on the ratio of areas and perimeters with these pdfs.

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Printable 7th Grade Math Worksheets

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Seventh grade math

IXL offers hundreds of seventh grade math skills to explore and learn! Not sure where to start? Go to your personalized Recommendations wall to find a skill that looks interesting, or select a skill plan that aligns to your textbook, state standards, or standardized test.

A. Integers

• 1 Understanding integers
• 2 Integers on number lines
• 3 Graph integers on horizontal and vertical number lines
• 4 Understanding absolute value
• 5 Absolute value and opposite integers
• 6 Quantities that combine to zero: word problems
• 7 Compare and order integers
• 8 Integer inequalities with absolute values

B. Operations with integers

• 1 Add integers using counters
• 2 Add integers using number lines
• 3 Integer addition rules
• 4 Add integers
• 5 Add three or more integers
• 6 Subtract integers using counters
• 7 Subtract integers using number lines
• 8 Integer subtraction rules
• 9 Subtract integers
• 10 Integer addition and subtraction rules
• 11 Add and subtract integers using counters
• 12 Add and subtract integers
• 13 Complete addition and subtraction equations with integers
• 14 Add and subtract integers: word problems
• 15 Understand multiplying by a negative integer using a number line
• 16 Integer multiplication rules
• 17 Multiply integers
• 18 Integer division rules
• 19 Equal quotients of integers
• 20 Divide integers
• 21 Integer multiplication and division rules
• 22 Multiply and divide integers
• 23 Complete multiplication and division equations with integers
• 24 Add, subtract, multiply, and divide integers
• 25 Evaluate numerical expressions involving integers

C. Decimals

• 1 Decimal numbers review
• 2 Compare and order decimals
• 3 Round decimals

D. Operations with decimals

• 1 Add and subtract decimals
• 2 Add and subtract decimals: word problems
• 3 Multiply decimals
• 4 Multiply decimals and whole numbers: word problems
• 5 Divide decimals
• 6 Divide decimals by whole numbers: word problems
• 7 Estimate sums, differences, and products of decimals
• 8 Add, subtract, multiply, or divide two decimals
• 9 Add, subtract, multiply, and divide decimals: word problems
• 10 Multi-step inequalities with decimals
• 11 Maps with decimal distances
• 12 Evaluate numerical expressions involving decimals

E. Number theory

• 1 Prime factorization
• 2 Greatest common factor
• 3 Least common multiple
• 4 GCF and LCM: word problems

F. Fractions

• 1 Understanding fractions: word problems
• 2 Equivalent fractions
• 3 Write fractions in lowest terms
• 4 Fractions: word problems with graphs and tables
• 5 Least common denominator
• 6 Compare and order fractions
• 7 Compare fractions: word problems
• 8 Convert between mixed numbers and improper fractions
• 9 Compare mixed numbers and improper fractions
• 10 Round mixed numbers

G. Operations with fractions

• 1 Add and subtract fractions
• 2 Add and subtract fractions: word problems
• 3 Add and subtract mixed numbers
• 4 Add and subtract mixed numbers: word problems
• 5 Inequalities with addition and subtraction of fractions and mixed numbers
• 6 Estimate sums and differences of mixed numbers
• 7 Multiply two fractions using models
• 8 Multiply fractions
• 9 Multiply mixed numbers
• 10 Multiply fractions and mixed numbers: word problems
• 11 Multiplicative inverses
• 12 Divide fractions
• 13 Divide mixed numbers
• 14 Divide fractions and mixed numbers: word problems
• 15 Estimate products and quotients of fractions and mixed numbers
• 16 Add, subtract, multiply, and divide fractions and mixed numbers: word problems
• 17 Maps with fractional distances
• 18 Evaluate numerical expressions involving fractions

H. Rational numbers

• 1 Convert fractions or mixed numbers to decimals
• 2 Convert decimals to fractions or mixed numbers
• 3 Convert between decimals and fractions or mixed numbers
• 4 Identify rational numbers
• 5 Classify rational numbers using a diagram
• 6 Classify rational numbers
• 7 Absolute value of rational numbers
• 8 Compare rational numbers
• 9 Put rational numbers in order
• 10 Classify real numbers

I. Operations with rational numbers

• 1 Add and subtract positive and negative decimals
• 2 Add and subtract positive and negative fractions
• 3 Add and subtract rational numbers
• 4 Rational numbers: find the sign
• 5 Apply addition and subtraction rules
• 6 Identify quotients of rational numbers: word problems
• 7 Multiply and divide positive and negative decimals
• 8 Multiply and divide positive and negative fractions
• 9 Multiply and divide rational numbers
• 10 Apply multiplication and division rules
• 11 Multi-step word problems with positive rational numbers

J. Exponents

• 1 Understanding exponents
• 2 Evaluate powers
• 3 Solve equations with variable exponents
• 4 Powers with negative bases
• 5 Powers with decimal and fractional bases
• 6 Powers of ten
• 7 Evaluate numerical expressions involving exponents
• 8 Scientific notation
• 9 Compare numbers written in scientific notation

K. Square roots

• 1 Square roots of perfect squares
• 2 Estimate square roots

L. Ratios, rates, and proportions

• 1 Understanding ratios
• 2 Identify equivalent ratios
• 3 Write an equivalent ratio
• 4 Equivalent ratios: word problems
• 5 Unit rates
• 6 Calculate unit rates with fractions
• 7 Compare ratios: word problems
• 8 Compare rates: word problems
• 9 Do the ratios form a proportion?
• 10 Do the ratios form a proportion: word problems
• 11 Solve proportions
• 12 Solve proportions: word problems
• 13 Estimate population size using proportions

M. Coordinate plane

• 1 Coordinate plane review
• 2 Quadrants and axes
• 3 Follow directions on a coordinate plane
• 4 Distance between two points

N. Proportional relationships

• 1 Find the constant of proportionality from a table
• 2 Write equations for proportional relationships from tables
• 3 Identify proportional relationships by graphing
• 4 Find the constant of proportionality from a graph
• 5 Write equations for proportional relationships from graphs
• 6 Identify proportional relationships from graphs and equations
• 7 Identify proportional relationships from tables
• 8 Complete a table and graph a proportional relationship
• 9 Graph a proportional relationship: word problems
• 10 Interpret graphs of proportional relationships
• 11 Write and solve equations for proportional relationships

O. Percents

• 1 What percentage is illustrated?
• 2 Convert between percents, fractions, and decimals
• 3 Compare percents to fractions and decimals
• 4 Estimate percents of numbers
• 5 Solve percent problems using strip models
• 6 Percents of numbers and money amounts
• 7 Percents of numbers: word problems
• 8 Solve percent equations
• 9 Solve percent equations: word problems
• 10 Percent of change
• 11 Percent of change: word problems
• 12 Percent of change: find the original amount word problems
• 13 Percent error: word problems

P. Consumer math

• 1 Add, subtract, multiply, and divide money amounts: word problems
• 2 Price lists
• 3 Unit prices
• 4 Unit prices with unit conversions
• 5 Unit prices: find the total price
• 6 Percent of a number: tax, discount, and more
• 7 Which is the better coupon?
• 8 Find the percent: tax, discount, and more
• 9 Sale prices: find the original price
• 10 Multi-step problems with percents
• 11 Estimate tips
• 12 Simple interest
• 13 Compound interest

Q. Units of measurement

• 1 Compare and convert customary units
• 2 Mixed customary units
• 3 Compare and convert metric units
• 4 Convert between customary and metric systems
• 5 Celsius and Fahrenheit temperatures

R. Expressions

• 1 Write variable expressions: one operation
• 2 Write variable expressions: two or three operations
• 3 Write variable expressions: word problems
• 4 Evaluate linear expressions
• 5 Evaluate multi-variable expressions
• 6 Evaluate absolute value expressions
• 7 Evaluate nonlinear expressions
• 8 Identify terms and coefficients
• 9 Sort factors of variable expressions

S. Equivalent expressions

• 1 Properties of addition and multiplication
• 2 Simplify expressions by combining like terms: with algebra tiles
• 3 Simplify expressions by combining like terms
• 4 Multiply using the distributive property: area models
• 5 Multiply using the distributive property
• 6 Write equivalent expressions using properties
• 7 Add and subtract linear expressions
• 8 Add and subtract like terms: with exponents
• 9 Factor linear expressions: area models
• 10 Factors of linear expressions
• 11 Identify equivalent linear expressions using algebra tiles
• 12 Identify equivalent linear expressions I
• 13 Identify equivalent linear expressions II
• 14 Identify equivalent linear expressions: word problems

T. One-variable equations

• 1 Which x satisfies an equation?
• 2 Write an equation from words
• 3 Solve equations using properties
• 4 Model and solve equations using algebra tiles
• 5 Write and solve equations that represent diagrams
• 6 Solve one-step equations
• 7 Solve two-step equations without parentheses
• 8 Solve two-step equations with parentheses
• 9 Solve two-step equations
• 10 Solve two-step equations with fractions
• 11 Choose two-step equations: word problems
• 12 Solve two-step equations: word problems
• 13 Solve equations involving like terms
• 14 Solve equations: complete the solution

U. One-variable inequalities

• 1 Solutions to inequalities
• 2 Graph inequalities on number lines
• 3 Write inequalities from number lines
• 4 Solve one-step inequalities
• 5 Graph solutions to one-step inequalities
• 6 One-step inequalities: word problems
• 7 Solve two-step inequalities
• 8 Graph solutions to two-step inequalities

V. Sequences

• 1 Identify arithmetic and geometric sequences
• 2 Arithmetic sequences
• 3 Geometric sequences
• 4 Sequences: mixed review
• 5 Sequences: word problems
• 6 Evaluate variable expressions for sequences
• 7 Write variable expressions for arithmetic sequences
• 1 Find the slope from a graph
• 2 Find the slope from two points
• 3 Find a missing coordinate using slope
• 4 Graph a line using slope
• 5 Constant rate of change
• 6 Rate of change: tables
• 7 Rate of change: graphs

X. Two-variable equations

• 1 Identify independent and dependent variables
• 2 Find a value using two-variable equations
• 3 Evaluate two-variable equations: word problems
• 4 Complete a table for a two-variable relationship
• 5 Write a two-variable equation
• 6 Identify the graph of an equation
• 7 Graph a two-variable equation
• 8 Interpret a graph: word problems
• 9 Write an equation from a graph using a table
• 10 Write a linear equation from a graph

Y. Lines and angles

• 1 Name, measure, and classify angles
• 2 Lines, line segments, and rays
• 3 Parallel, perpendicular, and intersecting lines
• 4 Identify complementary, supplementary, vertical, and adjacent angles
• 5 Find measures of complementary, supplementary, vertical, and adjacent angles
• 6 Write and solve equations using angle relationships
• 7 Identify alternate interior and alternate exterior angles
• 8 Transversals of parallel lines: name angle pairs
• 9 Transversals of parallel lines: find angle measures
• 10 Find lengths and measures of bisected line segments and angles

Z. Two-dimensional figures

• 1 Identify and classify polygons
• 2 Classify triangles
• 3 Triangle inequality
• 4 Identify trapezoids
• 5 Classify quadrilaterals I
• 6 Classify quadrilaterals II
• 7 Graph triangles and quadrilaterals
• 8 Find missing angles in triangles
• 9 Find missing angles in triangles using ratios
• 10 Find missing angles in quadrilaterals I
• 11 Find missing angles in quadrilaterals II
• 12 Interior angles of polygons
• 13 Parts of a circle
• 14 Central angles of circles

AA. Three-dimensional figures

• 1 Bases of three-dimensional figures
• 2 Nets of three-dimensional figures
• 3 Front, side, and top view
• 4 Cross sections of three-dimensional figures

BB. Perimeter and area

• 1 Perimeter
• 2 Area of rectangles and parallelograms
• 3 Area of triangles and trapezoids
• 4 Area and perimeter: word problems
• 5 Circumference of circles
• 6 Area of circles
• 7 Circles: word problems
• 8 Area of semicircles and quarter circles
• 9 Semicircles: calculate area, perimeter, radius, and diameter
• 10 Quarter circles: calculate area, perimeter, and radius
• 11 Area of compound figures made of rectangles
• 12 Area of compound figures with triangles
• 13 Area of compound figures with triangles, semicircles, and quarter circles
• 14 Area between two shapes

CC. Surface area and volume

• 1 Surface area of cubes and prisms
• 2 Surface area of pyramids
• 3 Lateral area of prisms and pyramids
• 4 Surface area of cylinders
• 5 Volume of cubes and prisms
• 6 Volume of cubes and rectangular prisms: word problems
• 7 Volume of prisms: advanced
• 8 Volume of pyramids
• 9 Volume of cylinders

DD. Scale drawings

• 1 Scale drawings of polygons
• 2 Scale drawings: word problems
• 3 Scale drawings: scale factor word problems
• 4 Perimeter and area: changes in scale

EE. Transformations

• 1 Identify reflections, rotations, and translations
• 2 Translations: graph the image
• 3 Translations: find the coordinates
• 4 Reflections over the x- and y-axes: graph the image
• 5 Reflections over the x- and y-axes: find the coordinates
• 6 Reflections: graph the image
• 7 Reflections: find the coordinates
• 8 Rotations: graph the image
• 9 Rotations: find the coordinates

FF. Congruence and similarity

• 1 Similar and congruent figures
• 2 Congruence statements and corresponding parts
• 3 Side lengths and angle measures of congruent figures
• 4 Side lengths and angle measures of similar figures
• 5 Similar figures and indirect measurement

GG. Data and graphs

• 1 Create line plots
• 2 Interpret line plots
• 3 Create and interpret line plots with fractions
• 4 Create stem-and-leaf plots
• 5 Interpret stem-and-leaf plots
• 6 Create bar graphs
• 7 Interpret bar graphs
• 8 Create histograms
• 9 Interpret histograms
• 10 Create frequency charts
• 11 Interpret circle graphs
• 12 Circle graphs and central angles
• 13 Box plots

HH. Statistics

• 1 Calculate mean, median, mode, and range
• 2 Interpret charts and graphs to find mean, median, mode, and range
• 3 Mean, median, mode, and range: find the missing number
• 4 Changes in mean, median, mode, and range
• 5 Calculate mean absolute deviation
• 6 Calculate quartiles and interquartile range
• 7 Identify an outlier
• • New! Populations and samples
• 8 Identify representative, random, and biased samples
• 9 Make inferences from multiple samples
• 10 Compare populations using measures of center and spread

II. Probability

• 1 Probability of simple events
• 2 Probability of simple events and opposite events
• 3 Probability of mutually exclusive events and overlapping events
• 4 Experimental probability
• 5 Make predictions using experimental probability
• 6 Use collected data to find probabilities and make predictions
• 7 Make predictions using theoretical probability
• 8 Compound events: find the number of outcomes
• 9 Compound events: find the number of sums
• 10 Find the number of outcomes: word problems
• 11 Probability of compound events
• 12 Which simulation represents the situation?
• 13 Identify independent and dependent events
• 14 Probability of independent and dependent events

Seventh grade lessons

These lessons help you brush up on important math topics and prepare you to dive into skill practice!

• Absolute value
• Additive inverses
• Adding and subtracting integers
• Multiplying and dividing integers
• Adding decimals
• Subtracting decimals
• Multiplying decimals by powers of 10
• Multiplying decimals by whole numbers
• Multiplying decimals
• Dividing decimals by powers of 10
• Dividing decimals by whole numbers
• Dividing decimals
• Rational numbers
• Comparing rational numbers
• Adding and subtracting rational numbers
• Multiplying and dividing rational numbers

Exponents and powers of 10

• Powers of 10

Properties and mixed operations

• The distributive property
• Order of operations

Percents, ratios, and rates

• Unit rates with fractions
• Simple interest
• Percent change

Proportions and proportional relationships

• Proportions
• Proportional relationships
• Constant of proportionality
• Expressions and equations
• Writing algebraic expressions
• Evaluating expressions
• Equivalent expressions
• Simplifying expressions
• Expanding expressions
• Factoring expressions
• Solving equations
• Multi-step equations
• Independent and dependent variables
• Inequalities on a number line
• Solving inequalities
• Area of triangles
• Area of parallelograms
• Area of rhombuses
• Area of trapezoids
• Parts of a circle
• Area of circles
• Circumference of circles
• Complementary angles
• Supplementary angles
• Adjacent angles
• Vertical angles
• What is surface area?
• Surface area formulas
• Volume formulas
• Volume of rectangular prisms
• Volume of prisms
• Volume of cylinders
• Volume of pyramids
• Cross sections
• Triangle inequality theorem

7 th Grade Math Worksheets

Free, Printable Math Worksheets for at-home Practice

A Parent’s Guide to Seventh Grade Math + Practice Worksheets

Download this informative guide to learn how to best support your seventh grader as they learn and master important seventh grade math concepts.

Free Practice Worksheets

Choose a Grade

Click on a concept below to try a sample question

Ratio & Proportion

Number system.

Probability

Why 7th grade math worksheets are important.

A stated objective of Common Core State Standards (CCSS) is to standardize academic guidelines nationwide. In other words, what Seventh Graders learn in math in one state should be the same as what students of the same age are learning in another state. The curricula may vary between these two states, but the general concepts behind them are similar. This approach is intended to replace wildly differing guidelines among different states, thus eliminating (in theory) inconsistent test scores and other metrics that gauge student success.

An increased focus on math would seem to include a wider variety of topics and concepts being taught at every grade level, including Seventh Grade. However, CCSS actually calls for fewer topics at each grade level. The Common Core approach (which is clearly influenced by “Singapore Math”—an educational initiative that promotes mastery instead of memorization) goes against many state standards. Many states mandate a “mile-wide, inch-deep” curriculum in which children are taught so much in a relatively short time span, that they aren’t effectively becoming proficient in the concepts they truly need to understand to succeed at the next level. Hence, CCSS works to establish an incredibly thorough foundation not only for the math concepts in future grades, but also toward practical application for a lifetime.

How Our Seventh Grade Math Worksheets Reflect Common Core Standards

In Seventh Grade, CCSS recommends that instructional time should focus on four critical skills. Thinkster worksheets for seventh grade have been designed to cater to these skills:

• Developing understanding of and applying proportional relationships
• Developing understanding of operations with rational numbers and working with expressions and linear equations
• Solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume
• Drawing inferences about populations based on samples

7th Grade Math Worksheets: Critical Areas of Focus

Seventh grade is very much a transition year for math. Much will be expected this year from students—after all, this is middle school, and the level of instruction, as well as the level of expectations, has increased. Yet, seventh graders will also discover that their hard work in previous years has left them well-prepared for this year’s math. For example, the concepts of ratio and unit rates introduced in seventh grade evolve into calculating the constant of proportionality in tables, graphs, equations, and diagrams in seventh. Here are four critical areas of focus, straight from Common Core, that will be emphasized in seventh grade:

Proportional Relationships

As already stated, ratios and proportions are a fluency requirement for seventh grade. Some of the focus will include real-world situations such as tax, discounts, tips, and other percentage problems. Students will solve problems about scale drawings, will graph proportional relationships and learn about slope, and distinguish proportional relationships from other relationships.

Rational Numbers, Expressions and Linear Equations

Students will understand that fractions, decimals, and percentages are different representations of rational numbers. Furthermore, they will extend their mastery of the four basic operations (addition, subtraction, multiplication, and division) to rational and negative numbers as well as expressions and equations involving one variable.

Scale Drawings, Informal Geometric Constructions, and Cross Sections of Twoand Three-Dimensional Shapes

Seventh graders will continue to work with area, including circumference and the surface area of three-dimensional objects. Congruence and similarity are on the horizon in Grade 8, and to prepare for that, students will reason about relationships using scale drawings and informal geometric constructions, as well as the relationship between angles and intersecting lines. They will also work with three-dimensional figures by examining two-dimensional cross sections, and they will solve real-world problems involving area, surface area, and volume.

Drawing Inferences on Populations Based on Samples

Having previously worked on single data distributions in Sixth Grade, seventh graders will compare two data distributions and answer questions about the differences of the populations. Also, they informally will work with random sampling to generate data sets and learn about drawing inferences based on representative samples. Seventh Grade : Introduction, Common Core State Standards Initiative. -->

Overview of Seventh Grade Math Topics

Though they may have seem detailed, the four areas of focus presented in the previous section are more just starting points of what seventh graders can expect during this crucial school year. From those areas, teachers and students will delve into more specific concepts that will prepare kids for eighth grade math and beyond. The five topics presented here, taken directly from CCSS 4 itself, include some details on what kids will be taught in seventh grade.

Ratios and Proportional Relationships

• Analyze proportional relationships and use them to solve realworld and mathematical problems. By the end of seventh grade, students will become experts in ratios and proportions. The concepts and activities in store for them include:

• Computing unit rates of ratios associated with fractions. For example, if you swim 1/4 of mile in 1/10 of an hour, a complex fraction of 1/4 / 1/10 miles, or 2.5 miles, per hour can be computed.
• Deciding whether two quantities are in a proportional relationship. This can be achieved by testing for equivalent ratios in a table or graphing on a coordinate plane and looking for a straight line through the origin.
• Identifying the constant proportionality—the unit rate—in tables, graphs, equations, diagrams, verbal descriptions, and word problems.
• Representing proportional relationships by equations. For example, if the total cost (t) of something is proportional to the number of items purchased (n) at one constant price (p), the relationship between the total cost and the number items can be described as t=pn.
• Explaining what a point (x,y) on a graph of a proportional relationship means in terms of the situation, especially to the points (0,0) and (1,r) in which r is the unit rate.
• Using proportional relationship to solve multi-step real-world problems. For example, if you paid $50 at a restaurant, and that total included a 20 percent tip, how much did you just pay for dinner itself before tipping?

Seventh Grade: Introduction, Common Core State Standards Initiative.

The Number System

• Apply and extend previous understandings of operations with fractions. Rational numbers also are emphasized with this topic, and students will understand how the additive property intertwines with this concept. Some areas taught include:

• Adding and subtracting rational numbers (any number that can be written as a simple fraction, in which the denominator is not 0), and, from students’ understanding of fractions, applying these operations by using a number line.
• Describing situations in which opposite quantities combine to make 0, which is an additive inverse. For example, spending $50 to pay off a negative account balance of -$50 to reach 0.
• The knowledge of absolute value is extended: Understanding that p+q as the number located a distance |q| from p in a positive or negative direction (depending on if q was positive or negative).
• Understanding that subtracting rational numbers is the same as adding the additive inverse. For example, 7 - 4 = 7 + (-4).
• Dividing and multiplying rational numbers, and understanding that (-1)(-1)=1 and that -(p/q) = (-p)/q = p/(-q).
• Converting a rational number to a decimal using long division, and the concept of repeating decimals.
• Solving real-world problems involving rational numbers using the four basic operations.

Expressions and Equations

• Use properties of equations to generate equivalent expressions. Students will apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. Also, they will discover that rewriting an expression or equation in a different form (for example, x + 0.1 = 1.1x is the same as increasing a number by 10 percent and is the same as multiplying by 1.1) can lead them to a better understanding of the problem at hand

• Solve real-life mathematical problems using numeric and algebraic expressions and equations. The algebra continues. Seventh graders will learn to:

• Solve multi-step word problems with positive and negative rational numbers in any form (fractions, decimals, and whole numbers), and convert between forms when necessary (for example, if a business saw its profits increase by 10 percent in a year, it made 1/10 more money than last year).
• Solve word problems that lead to equations such as px+q=r or p(x+q)=r, in which p, q, and r are rational numbers. Student s will also learn to compare the algebraic solution to an arithmetic solution and identify the series of operations in each approach—for example, if a rectangle has a perimeter of 30 inches and a length of 10 inches, what is the area?
• Solve word problems involving inequalities; for example, a word problem that leads to the equation 2x + 5 < 25, so x < 10. Also, seventh graders will graph solution sets for inequalities—for example, if a pizza delivery driver makes $100 a week plus $2 per pizza, a student could graph how many pizzas the driver would need to deliver to make $175

• Draw, construct, and describe geometrical figures and describe the relationship between them. Students will solve problems involving scale drawings of geometric figures, will draw geometric shapes (by hand, with a ruler and compass, and with technology) with given conditions, and will describe two-dimensional figures resulting from slicing three-dimensional figures such as pyramids and rectangular prisms.

• Solve real-life and mathematical problems involving angle measure, area, surface, and volume. Seventh graders will master the formulas for area and circumference of circles and use this knowledge to solve problems. They will also work with different types of angles (supplementary, complementary, vertical, and adjacent) and solve problems involving volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Statistics and Probability

• Use random sampling to draw inferences about a population. Students will understand that statistics can be used to gain information about a population, and they will also be taught about random sampling. Furthermore, seventh graders will gather data from a random sample to draw inferences about a population with an unknown characteristic. For example, if a classroom has three more girls than boys in it, make an estimate about how many more girls are at the entire school.

• Draw informal comparative inferences about two populations. Simply put, students compare two groups and arrive at conclusions, including inferences based on variability. For example, if one cross country team averages 9-minute miles during practice and a second team averages 10-minute miles, what will happen if a runner logging 7-minute miles switches from the first team to the second?

• Investigate chance processes, and develop, use, and evaluate probability models. Though it may not appear so at first glance, probability nicely ties in to many other topics seventh graders are being taught. Among the concepts explored:

• Understanding that the probability of an event lies somewhere between 0 and 1— with near 0 being unlikely, around 1/2 as about even odds, and near 1 as likely.
• Collecting data to approximate the probability of a chance event. For example, rolling a die 300 times and estimating a 6 will come up about, but likely not exactly, 50 times.
• Developing a model for probability and explaining its results and discrepancies.
• Using organized lists, tree diagrams, tables, and simulation to arrive at probabilities of compound events. For example, if half of the students in a classroom have brown eyes, what is the probability that if you pick a random eight kids, five will have that eye color?

Surviving Middle School Math

Junior high is a crazy time for many students. Many self-contained middle schools (schools that aren’t K-8) present unique challenges academically and socially. The homework load is greater, the routines are completely different, and kids that seemed so young just a couple years earlier are now ... teenagers. Moreover, 67 percent of middle school teachers feel that math is the toughest subject for students to re-engage in after summer break, and 50 percent added that kids' math skills regress more than any other school subject. Combining these factors creates a situation daunting for students and parents alike. And perhaps nowhere is the challenge more acute than with middle school math. However, there’s no reason why students can’t thrive during these two critical years. What follows are several tips for middle schoolers and their parents to help them through this part of their math education.

Middle School Study Tips

• Be cool If you have been looking through this guide at the topics you can expect to learn for this school year, you may be understandably intimidated. However, the way Common Core is designed, you will get plenty of instruction, practice, and reinforcement with one concept before moving on.

Furthermore, you will discover that becoming good at a certain topic sets you up to succeed at the next. In many previous math curricula, teachers would move onto the next concept before many students felt they had mastered the last one. With Common Core, you can be confident you’ll be ready for whatever lies ahead.

• Practice When You Are Not Tired The homework loads of many students increase in middle school. However, your math capabilities are better suited for when you are most alert and less tired. Therefore, try to work on math homework in the later afternoon or early evening when you are at your freshest after school. Getting all your homework completed is important, but reading a book for a literature class won’t require the computing power from your brain that math will.

• Read the Question You might encounter math problems that appear intimidating, both on first glance and after you’ve read the question. No need to worry: Almost everything being thrown at you is stuff you have learned or are currently learning. Clear your mind and read the question again. Break down the problem by writing all the given information and relevant numbers. From there, work your way through the question on your path to the answer. Once you master this process, all those intimidating problems won’t seem so frightening.

• Check Your Work One helpful aspect of solving algebraic equations is that checking your work is easy: Simply plug in the answer into the variable of the original problem and do the math. This is a good habit to start with your homework because if you made a mistake, you have time to figure out what went wrong, which will help you all the more in the future. Furthermore, once you are proficient in checking your work accurately and quickly with your homework, you will naturally do the same on tests, possibly (and hopefully!) resulting in better grades because you are catching your mistakes before handing the test in.

• Keywords, Keywords, Keywords! One math strategy you likely learned in elementary school is to look for keywords when solving word problems. Keywords are simply clues within a word problem that guide you toward a solution. This strategy is just as applicable in middle school as it was when you were younger, maybe even more so as you work to solve multi-step problems. Moreover, with new concepts you are learning, a new set of words will be entering your math vocabulary. Look for terms such as save, rate, per, proportion, percentage, and compare in middle school word problems.

• Skip the Calculator You will encounter plenty of math in the coming years (especially in trigonometry and pre-calculus) that will require the use of a calculator. At this level, however, you should know how to perform almost every required operation without technological help. Skipping the calculator and figuring out problems by hand (for example, computing circumference by multiplying by 3.14) keeps your skills sharp, shows the teacher you are taking time to solve problems instead of taking a shortcut, and prepares you for tests on which a calculator isn't allowed.

• Math Everywhere Much of the math you are learning now can extend to rest of your life. Look for opportunities to practice your skills outside of school. For example, if you are watching a football game and see that a quarterback has completed 15 of 24 passes, try converting that number to a fraction and a percentage. Or, figure out what percentage a $5 tip on a $27 haircut is. Your math skills will help your realworld skills that when sharp, will improve your in-school math skills in turn.

• Ask for Help If you find yourself struggling with a specific concept or with math in general, by all means, seek help from your teacher. Educators want you to succeed, and they will do whatever they can to help you do so … but sometimes, you have to ask. Also, don’t be afraid to tell your parents that you are having a rough time. Most adults remember how challenging middle school math was, and your parents can provide encouragement, work with you and your teacher, or explore other options to get the help you need to succeed.

Parent Tips

Parenting a 12, 13, or 14 year old is already quite a task. Navigating middle school math only increases the challenge, as well as your possible level of stress. Arguing with your child about school work is counterproductive, so staying calm and working positively with him or her is essential, no matter how frustrated you may get. The time parents get with their growing children is short enough; you don’t want to spend the middle school years in a constant battle with your kids. Take a deep breath—you will survive math during these years. Here are some tips to keep your sanity along the way:

• Be cool This is sage advice for parents as well as students. The level of math education you and your child encounter in middle school is unlike anything you may have experienced before. Yet, students this age are ready to take their learning to another level the curricula wouldn’t include such content if they weren’t capable. Though there may be bumps along the way, your child can still reach the destination.

• Relearn the Math One reason parents are apprehensive to engage their middle schooler with his or her math homework is that they might be a few decades removed from the math itself. Most parents remember how to multiply, but they might not have a clue how to solve two variable inequalities. Middle school math isn’t so difficult that adults can’t relearn the concepts. Many websites are available that describe a variety of math topics, or if you can sneak in 20 minutes here and there, read your student’s textbook (just don’t let your kids catch you!). Once you understand the math a little more, you will be better able to help your child when he or she is struggling.

• Understand Common Core Irrespective of your opinions about Common Core, more than likely, your kids are learning in a curriculum following the standards. Therefore, understanding the goals, guidelines, and structure of CCSS ultimately will help as you support your middle schooler through these years of math. For example, your child may be learning methods and strategies to solve a problem that you have never encountered. Your first inclination might be to dismiss these approaches and not offer any support. However, knowing that Common Core aims to provide multiple methods so that students achieve a well-rounded mastery will give you clarity on why your child is learning something a certain way … and it may inspire you to learn this new strategy as well.

• Drill for Skills Find opportunities for your middle schooler to practice math outside of his or her schoolwork. Challenge your daughter to compute tips. Direct your son to figure out what percentage of a gallon of gas is tax (the tax price is usually on the pump). If you are stuck in traffic or driving to an afterschool activity, rapid-fire some problems and equations, such as converting fractions to decimals. A couple extra minutes here and there keeps kids’ minds actively focused on math skills, which will be sharpened for when they are testing or doing homework.

• Become Involved If you are concerned with how Common Core is being implemented at your school, the amount of homework being given, or anything else in the math classroom, then you should absolutely get involved. Talk to teachers and administrators. Attend committee meetings. Research the subject that has you concerned. Parents naturally will have opinions about the quality of their children’s education. Those opinions can affect dialogue and solutions, but only if you take action. Your middle schooler is working hard to get the best education possible. There’s no reason you shouldn’t do the same for your child.

• Seek Help for Your Child If your middle-schooler is consistently struggling with math, your first step should be to talk to his or her teacher, who can provide guidance on how those struggles can be overcome. From there, another step you might consider is finding outside help your child. Several online resources provide math tutelage, including worksheets and sample tests that conform to Common Core standards. Tutoring might be an option, too. Innovative iPad-based math software has emerged that combines the personalized approach of a tutor with today’s technology. These revolutionary programs also may feature a curriculum based on Common Core, thus ensuring your child’s learning at home is aligned with what he or she is learning at school

Tips for Helping Your Seventh Grader with These Seventh Grade Math Worksheets

In addition to the grade-specific standards it sets forth, Common Core also emphasizes eight “Standards of Mathematical Practice” that teachers at all levels are encouraged to develop in their students. Here are descriptions of these eight practices—designed to improve student performance—and how they apply to middle schoolers:

Make sense of problems and persevere in solving them

Students explain the problem to themselves and determine ways they can reach a solution. Then, they work at the problem until it’s solved. By middle school, for example, many word problems are multi-step, requiring more than one operation on the way to an answer. Students must take care to determine what these steps are, decide what strategies (including correspondences between equations, verbal descriptions, graphs and tables, and looking for regularity and trends) will be necessary to solve the problem, and work toward the solution.

Reason abstractly and quantitatively

Students decontextualize and contextualize problems. By decontextualizing, they break down the problem into anything other than the standard operation. By contextualizing, they apply math into problems that seemingly have none. Middle-schoolers who are decontextualizing may envision a fraction or decimal into unit rates—for example, a student working with the fraction 3/8 might picture three squares across a chessboard—to help solve a problem. Students who are contextualizing might break a polygon into several smaller shapes in order to compute the total area.

Construct viable arguments and critique the reasoning of others

Students use their acquired math knowledge and previous results to explain or critique their work or the work of others, analyzing and using counterexamples as necessary. Most middle-schoolers have already learned how to work with classmates to achieve a goal. Students might be encouraged not only to work with a group to solve a particularly challenging math problem, but also to present and explain their solution to the teacher and the class.

Encourage them to show their work

This suggestion can be read two ways. First, students will be encouraged to show how they arrived at an answer, especially within Common Core. Second, ask your children to show you their homework, particularly the challenging stuff. Explaining how a problem is solved is a basic CCSS tenet, so if your kids can be confident in explaining their work to you, they will carry that confidence into the classroom when the teacher asks for those same explanations.

Model with mathematics

This is just like it sounds: Students use math to solve real-world problems. For example, a national department store chain offers sales either in the form of percentages off retail price and by a flat dollar amount savings (and sometimes both). Middle-schoolers can use their knowledge of ratios and percentages to determine from which sales method they will save more.

Use appropriate tools strategically

Another self-explanatory practice: Students learn and determine which tools are best for the math problem at hand. For older kids, the tools may seem obvious—pencil, paper, calculator, protractor, and so on—but knowing when to use what is important. For example, graph paper can be a big help when solving variable inequalities.

Attend to precision

Students strive to be exact and meticulous—period. The math vocabulary introduced to middle-schoolers rapidly expanding, so students must be precise in their words as well as their numbers. Consider this example: An equation (x=1) is different than an expression (x-1) and an inequality (x>1). Middle-schoolers who know these definitions will have an easier time when working with the corresponding concepts.

Look for and make use of structure

Students will look for patterns and structures within math and apply these discoveries to subsequent problems. Take the equation x +5=10; to get an answer, 5 must be subtracted from both sides. This basic algebraic structure will apply to almost all equations middle-schoolers will encounter, no matter the operation or the number of variables. Once students recognize and master this structure, they will automatically think about both sides of the equation when solving.

Look for and express regularity in repeated reasoning

Students come to realizations—“aha” moments is a good term for these realizations—about the math operations that they are performing and use this knowledge in subsequent problems. For example, middle-schoolers may discover that tipping 15 percent is an easy computation: Figure out 10 percent of the bill, then take half of that and add to get 15 percent. In no time, they will want to figure out the tip when you are at a restaurant. 6 Standards for Mathematical Practice, Common Core State Standards Initiative. -->

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7th Grade Math Entire Curriculum

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7th Grade Math Unit 1 Number Sense Curriculum

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N-Gen Math™ 7

The full experience and value of eMATHinstruction courses are achieved when units and lessons are followed in order.  Students learn skills in earlier units that they will then build upon later in the course.  Lessons can be used in isolation but are most effective when used in conjunction with the other lessons in this course. All Lesson/Homework files, Spanish translations of those files, and videos are available for free.  Other resources, such as answer keys and more, are accessible with a paid  membership .

Each month August through May we release new resources for this course that are accessible with a Teacher Plus membership. We release new resources in unit order throughout the school year.  You can see a list of our new releases by visiting our  blog  and selecting the most recent newsletter.

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• Table of Contents for N-Gen Math 7 and Standards Alignment
• Unit 1 - Essential Review
• Unit 2 - Operations with Signed Numbers
• Unit 3 - Proportional Relationships
• Unit 4 - Percent
• Unit 5 - Linear Expressions
• Unit 6 - Linear Equations and Inequalities
• Unit 7 - Statistics
• Unit 7cc - Statistics
• Unit 8 - Probability
• Unit 8cc - Probability
• Unit 9 - The Geometry of Angles and Triangles
• Unit 10 - Geometric Measurement

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Math Olympiad for Class 7

Math olympiad for class 7 motivates students to stay ahead in this competitive world. Class 7 is considered to be the foundational stage for higher grades. Grade 7 Math Olympiad exam comprises problems related to functions, expression, powers, exponents and equations which are highly crucial in forming a base for coming years. It is also advantageous for scoring well in boards and various competitive exams.

Class 7 math olympiad advances students’ interest in mathematics and trains them for competitive challenges. Students competing in math olympiads can assess themselves on school, zonal, state, national and international levels. Time-management and problem-solving skills built through IMO preparation are pivotal for academic and career success.

IMO Class 7 Exam Pattern

The IMO exam organized by SOF aims to recognize and promote the mightiest math minds. The test is conducted as per the curriculum of ICSE, CBSE and various state boards. There are two levels of the IMO exam. All students from various school boards are eligible for the level-1 IMO exam. In level-1 IMO exam students have to answer 50 multiple-choice questions from 4 sections viz. Logical Reasoning, Mathematical Reasoning, Achievers Section and Everyday Mathematics.

• There are 15 questions of 1 mark each from Section-1 i.e., Logical Reasoning.
• 20 questions of 1 mark each from Section-2 i.e., Mathematical Reasoning.
• 10 questions of 1 mark each from Section-2 i.e., Everyday Mathematics.
• 5 questions of 3 marks each from Section-3 i.e., Achievers Section.

The duration of the class 7 level-1 IMO exam is 60 minutes and the total marks are 60. Students are required to qualify the level-1 IMO exam for appearing in level-2 IMO exam.

IMO Syllabus for Class 7

Class 7 math olympiad syllabus is formulated to improve the fundamental knowledge of students based on concepts related to exponents, powers, algebraic expressions, linear equations and so on. The section-wise detailed IMO syllabus of class 7 is as follows:

Section – 1: Verbal and Non-Verbal Reasoning.

Section – 2:

• Integers, Exponents and Powers
• Fractions and Decimals
• Algebraic Expressions
• Simple Linear Equations
• Lines and Angles
• The Triangle and its Properties, Symmetry, Congruence of Triangles
• Rational Numbers, Perimeter and Area
• Comparing Quantities
• Data Handling
• Visualizing Solid Shapes
• Practical Geometry.

Section – 3: The syllabus for this section is as per the topics provided in section–2.

Section – 4: This section comprises problems from topics covered in section – 2.

IMO Class 7 Study Material

Math Olympiad study material is a great means to head start IMO preparation. Preparing with these resources enables students to quickly apprehend important IMO concepts and topics. There are various books, worksheets and sample papers available for class 7 IMO preparation. Students can solve a variety of problems provided in these books and worksheets to learn complex problem-solving. Practicing tricky questions further improves the computational clarity of students. The questions present in these worksheets are similar to the type of questions asked in the IMO exam.

The worksheets provide hints and step-wise solutions to all problems for students to evaluate their preparation and progress. Students can prepare easily for the IMO exam by doing a time-bound practice with these worksheets. This will help them in managing the time during the IMO exam.

IMO Sample Papers for Class 7

Students can refer to the Math olympiad class 7 sample papers to expedite their IMO preparation. It is a great way to gain a deep knowledge of the olympiad topics, the pattern of exam and the marking scheme. With these sample papers, students can solve a wide variety of problems from previous year olympiad exams. Practicing these sample papers will also advance their conceptual understanding of the math topics taught in the previous academic years.

Class 7 math olympiad sample papers illustrate all solutions along with examples for strengthening the fundamentals of the subject. It is quite helpful for students to build a step-wise understanding of solving all problems on their own. Thus, preparing with sample papers is a smart way to achieve success in the olympiad exam. Download and practice the latest IMO sample paper for class 7 to know more about the IMO pattern and type of questions asked in the exam.

FAQs on Math Olympiad for Class 7

What is math olympiad for class 7.

Math Olympiad for class 7 is a competitive exam that promotes a child’s cognitive skills and mathematical abilities. In this exam students in class 7 compete with their peers at both national and international level to showcase their math talent. The syllabus for class 7 math olympiad exam is the same followed by ICSE, CBSE and various school boards. Students can register for a math olympiad exam either through their school or individually depending on the registration process of the organization that conducts it.

How to register for Class 7 Math Olympiad?

Students studying in schools registered with SOF can obtain the registration forms and other necessary details from their schools. Students studying in schools not registered with SOF can obtain more details by visiting the official website of SOF.

How to Prepare for class 7 Math Olympiad?

The purpose of the IMO exam for class 7 is to test students’ capability to solve tricky problems related to numbers, computation operations, fractions, geometry, etc. Students in primary school levels have higher grasping power and thus it is relatively easy to teach them various olympiad concepts. A thorough practice of class 7 math olympiad, worksheets, books and other study materials will enable students to prepare well for the exam. It will also help them in gaining the right approach for facing competition on higher levels.

How to Solve Class 7 Math Olympiad Questions?

Time management is one of the primary requisites to solve class 7 math olympiad questions. Students should perform a time-bound practice of all MCQs present in the sample papers and mock tests to improve their computational speed for solving these problems. It will give them an insight into how much time they will require to solve each question so that they can attempt the easier sections first and spend more time on the complex ones later.

What are the Benefits of Participating in class 7 Math Olympiad Exams?

Participating in class 7 math Olympiad benefits students in many ways. Students who prepare for the math olympiad also perform better in their academics. Since the IMO exam is held on national and international levels, it offers a fantastic opportunity for students to compete with their peers. This also improves their self-esteem and confidence. The toppers of the IMO exam are felicitated with scholarships, cash prizes, medals, and recognition on international levels.

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Harris cautiously rolls out policy, aiming to outmaneuver Trump and address 2020 liabilities

Democratic presidential nominee Vice President Kamala Harris speaks at a campaign rally, Saturday, Aug. 10, 2024, in Las Vegas. (AP Photo/Julia Nikhinson)

Democratic presidential nominee Vice President Kamala Harris, center, arrives to board Air Force Two at San Francisco International Airport, Sunday, Aug. 11, 2024, in San Francisco. (AP Photo/Julia Nikhinson, Pool)

FILE - A tip jar contains one dollar and five dollar bills, Sept. 6, 2017 in New York. (AP Photo/Mark Lennihan, File)

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WASHINGTON (AP) — Vice President Kamala Harris is trying to outmaneuver former President Donald Trump and address old vulnerabilities on her policy positions as she starts to fill in how she would govern if elected in November.

Vice presidents rarely have policy portfolios of their own — and almost always set aside any views that differ from those of the Oval Office occupant. Now, after four years of following President Joe Biden’s lead, Harris is taking a cautious approach to unveiling a policy vision in her own right.

But her surprise ascendance to the top of the ticket after Biden dropped his reelection bid also means her policy platform is being pulled together just as quickly.

When Harris inherited Biden’s political operation in late July, the campaign’s website was quietly scrubbed of the six-point “issues” page that framed the race against Trump, including expanding voting protections and restoring nationwide access to abortion. Instead, Harris has peppered her speeches — so far heavy on biography for herself and her running mate — with broad goals like “building up the middle class.” She has called for federal laws to provide abortion access and ban assault-style weapons, but has been thin on the details of what specifically they would entail or how she would persuade Congress to make progress on some of the most hot-button political issues.

Asked by reporters on Saturday when she would unveil her policy platform, Harris promised more details this week and added, “It’ll be focused on the economy and what we need to do to bring down costs and also strengthen the economy overall.”

The first major window into her thinking came this past weekend, with a proposal pulled not from the policy backwaters of the Biden administration or the cutting-room floor of the legislative process but from her rival: Trump.

Harris announced that she, like Trump, wants to end federal taxation of tipped earnings for workers — with the added caveat that she would limit the plan to those in the lower- and middle incomes. The idea has drawn bipartisan support in recent months and is particularly salient in service industry-heavy Nevada.

It’s also one of the most prominent ideas embraced by Trump in his 2024 bid to get back into the White House — a bonus in the view of the Harris camp, which has tried to needle the Republican into making unforced errors.

The Republican was none too amused by Harris endorsing the idea, complaining on his social media platform that “This was a TRUMP idea - She has no ideas, she can only steal from me.”

Trump continued on the matter in an interview with Elon Musk on Monday night, criticizing Harris for adopting his idea after what he claimed was harassment by the Biden administration of tipped workers.

On Monday, the White House said that Biden backed the plan too, though White House press secretary Karine Jean-Pierre wouldn’t address why Biden and Harris didn’t push for it during their first three-and-a-half years in office.

“Obviously, it’s a new idea,” she said, but added later in response to criticism from Trump, “Why didn’t they pass it during the last administration?”

In her first weeks as a candidate, Harris’ most pronounced policy moves have been to back away from liberal stances she took in her failed 2020 bid for the White House, including proposals to ban fracking, establish a single-payer healthcare system and decriminalize illegal border crossings. Harris dropped out of that heated race before a single vote had been cast but recognizes that voters now could punish her for those stances if not quickly addressed.

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Another complication for Harris comes from her relationship with Biden, who quickly endorsed her and handed her the keys to his political operation after he dropped out.

“The last three and a half years, they’ve been in sync,” said Jean-Pierre. “They have been certainly on the same page. And I presume that that will continue from here.”

Biden himself only began outlining detailed policy ideas for a second term during his final, frenzied effort to salvage his candidacy after his disastrous June 27 debate against Trump. He advocated for restoring abortion access, raising the federal minimum wage and passing a new surtax on billionaires. Harris has largely embraced all those priorities, including the incumbent’s call for changes to the Supreme Court.

But all those plans would require congressional support, which proved elusive even when Democrats held unified control of Washington during the first two years of the Biden-Harris administration.

Harris’ campaign, meanwhile, suggested that her attempted shifts to the center are reflective of how she would try to bring consensus to government.

“While Donald Trump is wedded to the extreme ideas in his Project 2025 agenda, Vice President Harris believes real leadership means bringing all sides together to build consensus,” said Harris spokesman Kevin Munoz. “It is that approach that made it possible for the Biden-Harris administration to achieve bipartisan breakthroughs on everything from infrastructure to gun violence prevention. As President, she will take that same pragmatic approach, focusing on common-sense solutions for the sake of progress.”

While Trump in recent weeks has resorted to personal and racially tinged attacks on his new rival, his campaign has been working to put Harris’ policy aims front and center, aiming to paint Harris as a radical liberal, pointing to old videos of her discussing policy positions during the 2020 Democratic primary.

“Kamala Harris has flip-flopped on virtually every policy she has supported and lived by for her entire career, from the Border to Tips, and the Fake News Media isn’t reporting it,” Trump posted Sunday. “She sounds more like Trump than Trump, copying almost everything. She is conning the American public, and will flip right back. I will MAKE AMERICA GREAT AGAIN! There will be no flipping!!!”

Associated Press writers Jill Colvin and Darlene Superville contributed to this report.

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Fact-Checking Claims About Tim Walz’s Record

Republicans have leveled inaccurate or misleading attacks on Mr. Walz’s response to protests in the summer of 2020, his positions on immigration and his role in the redesign of Minnesota’s flag.

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By Linda Qiu

Since Gov. Tim Walz of Minnesota was announced as the Democratic nominee for vice president, the Trump campaign and its allies have gone on the attack.

Mr. Walz, a former teacher and football coach from Nebraska who served in the National Guard, was elected to the U.S. House of Representatives in 2006 and then as Minnesota’s governor in 2018. His branding of former President Donald J. Trump as “weird” this year caught on among Democrats and helped catapult him into the national spotlight and to the top of Vice President Kamala Harris’s list of potential running mates.

The Republican accusations, which include questions over his military service , seem intended at undercutting a re-energized campaign after President Biden stepped aside and Ms. Harris emerged as his replacement at the top of the ticket. Mr. Trump and his allies have criticized, sometimes inaccurately, Mr. Walz’s handling of protests in his state, his immigration policies, his comments about a ladder factory and the redesign of his state’s flag.

Here’s a fact check of some claims.

What Was Said

“Because if we remember the rioting in the summer of 2020, Tim Walz was the guy who let rioters burn down Minneapolis.” — Senator JD Vance of Ohio, the Republican nominee for vice president, during a rally on Wednesday in Philadelphia

This is exaggerated. Mr. Walz has faced criticism for not quickly activating the National Guard to quell civil unrest in Minneapolis in the summer of 2020 after the murder of George Floyd by a police officer. But claims that he did not respond at all, or that the city burned down, are hyperbolic.

Mr. Floyd was murdered on May 25, 2020, and demonstrators took to the streets the next day . The protests intensified, with some vandalizing vehicles and setting fires. More than 700 state troopers and officers with the Minnesota Department of Natural Resources’ mobile response team were deployed on May 26 to help the city’s police officers, according to a 2022 independent assessment by the state’s Department of Public Safety of the response to the unrest.

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