# Grade 7 Common Core Math Curriculum

## Grade 7 Common Core Math Curriculum

#### Listed below are Math quizzes for 7th grade students based on the Common Core Math State Standards.

For grade level assignments, we adhere to the Common Core State Standards Initiative's curriculum, in addition to considering other course curriculums such as GCSE(UK), Singapore Math, Australian and Indian Math curriculums. These courses will help students to perform well in local and major international competitions such as the Science Bee, Math Olympiad, American Mathematics Competition and so on.

In grade 7, the focus is on four critical areas, namely

1) understanding and applying proportional relationships

2) operations with rational numbers and working with expressions and linear equations

3) solving scale drawings, geometric constructions, and two and three-dimensional shapes to solve area and volume problems

4) drawing inferences about populations based on samples

Some of the mathematical practices that will be covered are:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

### Grade 7: Ratios and Proportional Relationships

You will use your previous understanding of ratios that you learned in the 6th grade and now apply them to solving proportionality problems that involve either single or multi-step.

You will be solving percent problems including those involving discounts, interest, taxes, tips, and percent increase or decrease.

You will be solving problems about scale drawings by relating corresponding lengths between the objects. You will be using the fact that relationships of lengths within an object are preserved in similar objects.

You will graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope.

You will be able to distinguish proportional relationships from other relationships.

7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

Working with Unit Rates

Solve Unit Rates

Using Unit Rates to Solve Fraction Problems

7.RP.A.2A Recognize and represent proportional relationships between quantities.

Understanding and Representing Proportions

Find Equivalent Ratios

Determine Proportional Relationship in Tables

7.RP.A.2B Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Find Constant of Proportionality

Solve Proportionality Problems Using Y=KX

Find the Constant of Proportionality Using Graphs

Find the Constant of Proportionality Using Tables

7.RP.A.2C Represent proportional relationships by equations.

Write Proportional Equations

7.RP.A.2D Explain what a point (xy) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Interpret Graphs for Proportions

7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems.

Solving Multi-Step Ratio and Percent Problems

### Grade 7: The Number System

You will develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers.

You will extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division.

By applying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), you should be able to explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers.

You will use the arithmetic of rational numbers as you formulate expressions and equations in one variable and use these equations to solve problems.

7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.A.1B Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

Identify the Sum on a Number Line

Find Distance Using Number Line

7.NS.A.1C Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

Convert Subtraction Expression Into Addition Expression

Adding Inverse and Distance Between Points on a Number Line

Find Equivalent Expressions for Expressions with Negative Numbers

7.NS.A.1D Apply properties of operations as strategies to add and subtract rational numbers.

Strategies to Add and Subtract Rational Numbers

7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers..

Rational Numbers (Multiplication/Division)

7.NS.A.2A Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

Division of Rational Numbers

7.NS.A.2B Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

Expressing Rational Numbers as Quotients of Integers

Division with Negative Numbers

Multiplication with Negative Numbers

7.NS.A.2C Apply properties of operations as strategies to multiply and divide rational numbers.

Strategies to Divide and Multiply Rational Numbers

Multiply Rational Numbers Using Commutative Property

7.NS.A.2D Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Convert Rational Number into a Decimal

Check the Fraction for Terminating or Repeating Decimal

7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

Solving Real-World Rational Number Problems

### Grade 7: Expressions and Equations

Here, you will use the arithmetic of rational numbers as you formulate expressions and equations in one variable and use these equations to solve problems.
7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Strategies to Add, Subtract, Factor, and Expand Linear Expressions

Expand Expressions

Factor Expressions

Simplify Expressions

7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

Rewriting an Expression

Rewrite Percent Word Problems as Decimal Expressions

7.EE.A.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies.

Modeling Using Equations

Solve Percent and Decimal Problems

7.EE.A.4 Use variables to represent quantities in a real-world or mathematical problem and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Solving Multi-Step Problems Using Equations

7.EE.A.4A Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where pq, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Solve Equations of the Form px + q = r and p(x + q) = r

7.EE.A.4B Solve word problems leading to inequalities of the form px + q > r or px + q < r, where pq, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem.

Solve Inequalities of the Form px+ q < r

Here, you will continue your work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects.

In preparation for work on congruence and similarity in Grade 8 you will reason about relationships among two-dimensional figures using scale drawings and informal geometric constructions, and you will gain familiarity with the relationships between angles formed by intersecting lines.

You will work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections.

You will solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.

7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Solve Problems Involving Scale Drawings of Shapes

Find the Area of Scaled Rectangles

7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Drawing Plane Figures

Check Feasibility of Triangle Based on Sides and Angles

7.G.A.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Identify Cross Sections of 3D Figures

7.G.A.4 Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle..

Finding Area and Circumference of Circles

7.G.A.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

Finding Angles

7.G.A.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Finding Area, Volume, and Surface Area

### Grade 7: Statistics and Probability

You will build on your previous work with single data distributions to compare two data distributions and address questions about differences between populations.

You will begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.

7.SP.A.1 Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

Sampling a Population

7.SP.A.2 Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

Making Inferences from Random Data

7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.

Comparing Distributions

7.SP.A.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Mean, Median, Mode and Range

7.SP.A.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

Understand the Probability of a Single Event

7.SP.A.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

Predicting Using Profitability

7.SP.A.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

Developing a Probability Model

7.SP.A.7A  Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.

7.SP.A.7B Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

7.SP.A.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
Determine Probability of Compound Events
7.SP.A.8A Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

7.SP.A.8B Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

7.SP.A.8C Design and use a simulation to generate frequencies for compound events.