## CONTENTS Beginning of Intermediate School and on the brink of their teenage years, Grade 7 helps a child discover his/her true personality. This is also the year where academic competition starts to rise and directions towards future careers begin to be mapped. Strengthening of mathematics concept in this grade also becomes imperative. Moving from the world of basic decimals and fractions, Grade 7 further explores the number system and proportional relationships and introduces the concepts of transformations and congruence. ## Number theory The study of whole numbers and their properties is called Number theory. Number theory is a large and interesting area in mathematics, including studying Prime numbers, rational numbers and so on. Number theory is important because it helps you to understand and master how the numbers function which helps with logical reasoning skills.

Prime or composite

Prime factorization

Multiplicative inverses

Divisibility rules

Greatest common factor

Least common multiple

GCF and LCM: word problems

Scientific notation

Compare numbers written in scientific notation

Classify numbers

## Integers Integers are like whole numbers which means they do not have fraction or decimal part but unlike whole numbers they can be negative. Understanding integers will help you to understand that negative and positive numbers are used together to describe quantities having opposite direction or values.

Understanding integers

Integers on number lines

Graph integers on horizontal and vertical number lines

Absolute value and opposite integers

Compare and order integers

Integer inequalities with absolute values

## Operations with integers Four basic operations with integer numbers. In the primary grades, students develop an understanding of part-whole concepts – they learn that two or more parts can be combined to create a whole (addition) or they can be separated from a whole (Subtraction). The multiplication of numbers is repeated addition. Separation of partitioning of objects from a set for an equal share without any disparity in the fixed number of groups.

Add and subtract integers using counters

Complete addition and subtraction sentences with integers

Add and subtract integers: word problems

Integer multiplication and division rules

Multiply and divide integers

Complete multiplication and division sentences with integers

Evaluate numerical expressions involving integers

## Decimals A number that has a decimal point followed by digits that show a value smaller than one.

Decimal numbers review

Compare and order decimals

Decimal number lines

Round decimals
II

## Operations with decimals Four basic operations on decimal numbers are like whole numbers but with a difference of understanding how the decimal point is affecting the operations. For example, just need to do the multiplication without the decimal then insert the decimal in the right spot.

Add and subtract decimals: word problems

Multiply decimals

Multiply decimals and whole numbers: word problems

Divide decimals

Divide decimals by whole numbers: word problems

Estimate sums, differences and products of decimals

Add, subtract, multiply and divide decimals: word problems

Multi-step inequalities with decimals

Maps with decimal distances

Evaluate numerical expressions involving decimals

## Fractions and mixed numbers Fractions help us to understand how many equal parts of a whole we have.

Understanding fractions: word problems

Equivalent fractions

Write fractions in lowest terms

Fractions: word problems with graphs and tables

Least common denominator

Compare and order fractions

Compare fractions using benchmarks

Compare fractions: word problems

Convert between mixed numbers and improper fractions

Compare mixed numbers and improper fractions

Round mixed numbers

Put a mix of decimals, fractions and mixed numbers in order We can add or subtract fractions like the normal numbers if their denominators are equal. If the denominators are not equal, we have to change it by multiplying or dividing but we have to apply the same to the top (numerators).

Add and subtract fractions with like denominators

Add and subtract fractions with like denominators: word problems

Add fractions with unlike denominators using models

Subtract fractions with unlike denominators using models

Subtract fractions with unlike denominators

Add and subtract fractions with unlike denominators: word problems

Add and subtract mixed numbers: word problems

Inequalities with addition and subtraction of fractions and mixed numbers

Estimate sums and differences of mixed numbers

## Multiply fractions Multiplying the fractions is quite easy, you have to just multiply the numerators and denominators to each other and at the end just simplify the fraction if needed.

Multiply unit fractions by whole numbers using number lines

Multiply unit fractions by whole numbers using models

Multiply fractions by whole numbers using number lines

Multiply fractions by whole numbers using models

Multiply fractions and whole numbers

Multiply fractions and whole numbers: word problems

Multiply two fractions using models

Multiply fractions

Multiply fractions: word problems

Multiply three or more fractions and whole numbers

## Divide fractions To divide the fractions, you need to upside down the second fraction and then multiply them together

Divide whole numbers by unit fractions using models

Reciprocals

Divide whole numbers and unit fractions

Divide whole numbers by fractions

Divide fractions

Divide fractions: word problems

## Rational numbers A Rational number is made by dividing two integers (integer is a number with no fraction or decimal part). Most of the numbers we use in everyday life are rational numbers. If you can write a number as a simple fraction, then it is a rational number.

Identify rational numbers

Convert between decimals and fractions or mixed numbers

Absolute value of rational numbers

Compare rational numbers

Put rational numbers in order

Multiply and divide rational numbers

Apply multiplication and division rules

Estimate products and quotients of rational numbers

Add, subtract, multiply and divide rational numbers: word problems

Evaluate numerical expressions involving fractions

## Exponents and square roots The exponent of a number tells us how many times to multiply that number with itself. It is written as a small number to the right and above the base number.

Understanding exponents

Evaluate exponents

Solve equations with variable exponents

Exponents with negative bases

Exponents with decimal and fractional bases

Evaluate numerical expressions involving exponents

Square roots of perfect squares

Estimate square roots

## Ratios, rates and proportions A ratio shows the relative sizes of two or more values, in other words a Ratio compares values. A ratio says how much of one thing there is compared to another thing. For example, if there is 1 boy and 3 girls, we can write the ratio like 1:3 (for every 1 boy there are 3 girls.) Ratio, rates and proportion skills are useful to understand the association between two quantities.

Understanding ratios

Identify equivalent ratios

Write an equivalent ratio

Equivalent ratios: word problems

Unit rates

Compare ratios: word problems

Scale drawings: word problems

Do the ratios form a proportion?

Do the ratios form a proportion: word problems

Solve proportions

Solve proportions: word problems

Estimate population size using proportions

Rate of change

Constant rate of change

## Proportional relationships Proportion says that two ratios or fractions are equal. When quantities have the same relative size when say they have proportional relationship; or in other word they have the same ratio. Understanding of ratios and proportional relationships is very important to enhance math skills of fractions, decimals, rates, and etc.

Find the constant of proportionality from a table

Write equations for proportional relationships from tables

Identify proportional relationships by graphing

Find the constant of proportionality from a graph

Write equations for proportional relationships from graphs

Identify proportional relationships

Interpret graphs of proportional relationships

Write and solve equations for proportional relationships

## Percents “Percent” comes from the Latin Per Centum. The Latin word Centum means 100. When we say Percent, we mean per 100, so 1 percent means 1 per 100. We use the symbol % to show the percent. For example, 50% means 50 per 100. Understanding percentages is important for math skills and real life, for example stores advertise discounts on their products by using percents, like 30% off on math books.

What percentage is illustrated?

Convert between percents, fractions and decimals

Compare percents to fractions and decimals

Estimate percents of numbers

Percents of numbers and money amounts

Percents of numbers: word problems

Solve percent equations

Solve percent equations: word problems

## Consumer math Consumer math is about learning spending money skills by using basic math skills such as basic operations, percent and other skills. Consumer math is an important skill for everyday life, you will learn how to calculate sale prices, tax and interests.

Add, subtract, multiply and divide money amounts: word problems

Price lists

Unit prices

Unit prices: find the total price

Percent of a number: tax, discount and more

Find the percent: tax, discount and more

Sale prices: find the original price

Multi-step problems with percents

Estimate tips

Simple interest

Compound interest

## Problem solving and estimation A question that needs a solution. In mathematics some problems use words, so you need to learn how to interpret them into mathematical expressions and find the appropriate answer to the question. Problem solving is important skill in life which helps you to tackles the problem in life and find the best solution for them. Sometimes when we try to find an answer to our question, we cannot find the exact answer, so we estimate it. Estimation is the process of finding a value that is close enough to the right answer.

Estimate to solve word problems

Multi-step word problems

Guess-and-check word problems

Use Venn diagrams to solve problems

Find the number of each type of coin

Elapsed time word problems

## Units of measurement A quantity used as a standard of measurement; it is how much makes up “1” of the measurement. So, 1 second is a unit of time or the basic unit of length in metric is meter so 1 meter is a unit of length. Measurement provides a meaningful context for the use of number skills and spatial concepts.

Estimate metric measurements

Compare and convert metric units

Metric mixed units

Convert square and cubic units of length

Convert between cubic metres and litres

Precision

## Coordinate plane The plane containing X axis and Y axis is called coordinate plane. Cartesian coordinated can be used to pinpoint where we are on a map or graph. We can mark a point on a graph by how far along and how far up it is, the point (10,6) is 10 units along and 6 units up. Coordinate plane is exciting and important for learning math and it has important use in real life like mapping an area or arranging furniture in your room.

Coordinate plane review

Follow directions on a coordinate plane

Distance between two points

## Number sequences A pattern is a series or sequence that repeats. Mathematics patterns are sequences that repeat according to a rule or rules. Numbers can have interesting patterns, like Arithmetic sequences Geometric sequences and so on. Number sequence is a list of numbers in a special order.

Identify arithmetic and geometric sequences

Arithmetic sequences

Geometric sequences

Number sequences: mixed review

Number sequences: word problems

Evaluate variable expressions for number sequences

Write variable expressions for arithmetic sequences

## Expressions and properties Numbers, symbols and operators grouped together that show the value of something is called an expression. A variable is a symbol for a number we do not know yet. Understanding algebraic expressions help you to understand real life relationships and increase logical thinking skills.

Write variable expressions

Write variable expressions: word problems

Evaluate linear expressions

Evaluate multi-variable expressions

Evaluate absolute value expressions

Evaluate nonlinear expressions

Identify terms and coefficients

Sort factors of expressions

Multiply using the distributive property

Solve equations using properties

Write equivalent expressions using properties

Add, subtract and multiply linear expressions

Factors of linear expressions

Identify equivalent linear expressions

## One-variable equations An equation says that two things are equal, it will have an equal sign “=”. A variable is a symbol for a number we do not know yet. A single variable equation (one-variable equation) is an equation in which there is only one variable used. Note that the variable can be used multiple times or used on either side of the equation; all that matters is that the variable remains the same.

Which x satisfies an equation?

Write an equation from words

Model and solve equations using algebra tiles

Write and solve equations that represent diagrams

Solve one-step equations

Solve two-step equations

Solve equations: word problems

Solve equations involving like terms

Solve equations: complete the solution

## Two-variable equations An equation says that two things are equal, it will have an equal sign “=”. A variable is a symbol for a number we do not know yet. Two-variable equation is like single variable equation but there are two variables, to solve these types of equations you have to rewrite in such a way to eliminate one of the variables and then solve for the remaining variable.

Does (x, y) satisfy the equation?

Identify independent and dependent variables

Solve word problems involving two-variable equations

Complete a table for a two-variable relationship

Write a two-variable equation

Identify the graph of an equation

Graph a two-variable equation

Interpret a graph: word problems

Write an equation from a graph using a table

## Two-dimensional figures Two-dimensional geometry or plane geometry is about flat shapes like triangles and circles. Two-dimensional figures have only two dimensions such as width and height but no thickness. It also known as “2D”.

Identify and classify polygons

Name, measure and classify angles

Classify triangles

Identify trapezoids

Find missing angles in triangles and quadrilaterals

Interior angles of polygons

Lines, line segments and rays

Parallel, perpendicular and intersecting lines

Identify complementary, supplementary, vertical, adjacent and congruent angles

Find measures of complementary, supplementary, vertical and adjacent angles

Transversal of parallel lines

Find lengths and measures of bisected line segments and angles

Parts of a circle

## Transformations and congruence When we change a shape by using Turn, flip, slide or resize it is called transformation. If one shape can become another using Turn, Flip or Slide then shapes are congruent. Congruence keeps the size, area, angles and line lengths of the shape.

Symmetry

Identify reflections, rotations and translations

Translations: graph the image

Translations: find the coordinates

Reflections: graph the image

Reflections: find the coordinates

Rotations: graph the image

Rotations: find the coordinates

Similar and congruent figures

Side lengths and angle measures of congruent figures

Congruence statements and corresponding parts

Side lengths and angle measures of similar figures

Similar figures and indirect measurement

## Constructions Construction in Geometry means to draw shapes, angles or lines accurately. These constructions use only compass, straightedge and a pencil.

Construct the midpoint or perpendicular bisector of a segment

Construct an angle bisector

Construct a congruent angle

Construct a perpendicular line

Construct parallel lines

Construct an equilateral triangle or regular hexagon

## Three-dimensional figures Having three dimensions such as Height, Width and Depth, like any real-world object is a three-dimensional figure. Three-dimensional geometry is about solid shapes like spheres or cubes. It is also known as “3D”.

Bases of three-dimensional figures

Nets of three-dimensional figures

Front, side and top view

## Geometric measurement Geometric measurement is studying the properties of shapes by measuring them, like finding the Area or Perimeter of a shape.

Perimeter

Area of rectangles and parallelograms

Area of triangles

Area of trapezoids

Area with mixed numbers

Area and perimeter: word problems

Circles: calculate area, circumference, radius and diameter

Circles: word problems

Semicircles: calculate area, perimeter, radius and diameter

Quarter circles: calculate area, perimeter and radius

Area of compound figures with triangles, semicircles and quarter circles

Area between two shapes

Surface area

Perimeter, area and volume: changes in scale

## Data and graphs 1. BB.1 Interpret tables 2. BB.2 Interpret line plots 3. BB.3 Create line plots 4. BB.4 Interpret stem-and-leaf plots 5. BB.5 Create stem-and-leaf plots 6. BB.6 Interpret bar graphs 7. BB.7 Create bar graphs 8. BB.8 Interpret histograms 9. BB.9 Create histograms 10. BB.10 Create frequency charts 11. BB.11 Interpret circle graphs 12. BB.12 Circle graphs and central angles 13. BB.13 Interpret line graphs 14. BB.14 Create line graphs 15. BB.15 Interpret box-and-whisker plots 16. BB.16 Scatter plots 17. BB.17 Choose the best type of graph

Construct the midpoint or perpendicular bisector of a segment

Construct an angle bisector

Construct a congruent angle

Construct a perpendicular line

Construct parallel lines

Construct an equilateral triangle or regular hexagon

## Statistics Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of data. Statistics is a strong tool in everyday life to get answers about data and make concrete decisions.

Calculate mean, median, mode and range

Interpret charts to find mean, median, mode and range

Mean, median, mode and range: find the missing number

Changes in mean, median, mode and range

Identify representative, random and biased samples

## Probability Probability is the chance of something happening or how likely it is that some event will happen. Probability is a number between 0 (not happening) to 1 (certainly happening). Easiest way to understand probability is to toss a coin. There are two outcomes of tossing a coin namely Heads or Tails.

Probability of simple events

Probability of simple events – word problems

Probability of opposite, mutually exclusive and overlapping events

Experimental probability

Make predictions

Compound events: find the number of outcomes

Counting principle