## CONTENTS Grade 6 is a benchmark year for every child. Almost on the threshold of junior school, Grade 6 is the bridge between the foundations of elementary school and new concepts of junior school. This bridge makes it imperative for every Grade 6 students’ mathematics to be concrete and clear. Entering the world of ratios with the understanding of dimensions and basic fractions and decimals from Grade 5, Grade 6 elaborates on the applications of the basic concepts including the metric system, probability, fractions while introducing new facets of probability and graphs. ## Whole numbers In mathematics whole numbers are positive integers or nonnegative integers if you include zero. There is no fraction or decimal parts in whole numbers they also cannot be negative. Whole numbers are important because they are basic counting numbers.

Place values in whole numbers

Word names for numbers

Roman numerals

## Decimals A number that has a decimal point followed by digits that show a value smaller than one. Understanding decimal numbers is important to our daily lives as it relates to money, fractional amounts or metric measures.

What decimal number is illustrated?

Decimal place values

Word names for decimal numbers

Put decimal numbers in order

Inequalities with decimals

Round decimals

Round whole numbers and decimals: find the missing digit

Decimal number lines

## 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

Integers on number lines

Graph integers on horizontal and vertical number lines

Compare and order integers 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).

Add and subtract whole numbers up to millions

Add and subtract whole numbers: word problems

Estimate sums and differences of whole numbers

Estimate sums and differences: word problems

Add and subtract decimals: word problems

Estimate sums and differences of decimals

Maps with decimal distances

## Multiplication The multiplication of numbers can be seen as repeated addition. For example, 3×4 = 4+4+4. It is important to learn the basic operations for future math works.

Multiply whole numbers

Multiply whole numbers: word problems

Multiply numbers ending in zeroes

Multiply numbers ending in zeroes: word problems

Multiply three or more numbers

Multiply three or more numbers: word problems

Estimate products

## Division Separation of partitioning of objects from a set for an equal share without any disparity in the fixed number of groups. The resultant will be a whole number quotient and a remainder if the number is not divisible further.

Divisibility rules

Divide by two-digit numbers

Divide by two-digit numbers: word problems

Division patterns with zeroes

Divide numbers ending in zeroes: word problems

Estimate quotients

## Multiply and divide decimals Multiplying and dividing decimals is like the normal multiplication and division with one small difference aka decimals points. Just need to do the multiplication without the decimal then insert the decimal in the right spot.

Multiply a decimal by a one-digit whole number

Multiply a decimal by a multi-digit whole number

Multiply decimals and whole numbers: word problems

Multiply two decimals using grids

Multiply decimals

Estimate products of decimal numbers

Inequalities with decimal multiplication

Divide decimals by whole numbers

Divide decimals by whole numbers: word problems

Multiply and divide decimals by powers of ten

Division with decimal quotients

Inequalities with decimal division

## Exponents 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.

Write multiplication expressions using exponents

Evaluate exponents

Find the missing exponent or base

Exponents with decimal bases

## 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.

Prime or composite

Identify factors

Prime factorization

Prime factorization with exponents

Greatest common factor

Least common multiple

GCF and LCM: word problems

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

Fractions and mixed numbers review

Understanding fractions: word problems

Equivalent fractions review

Write fractions in lowest terms

Fractions of a group: word problems

Least common denominator

Compare fractions using models

Compare fractions with like and unlike denominators

Compare fractions: word problems

Convert between improper fractions and mixed numbers

Convert between decimals and fractions or mixed numbers

Graph and order fractions on number lines

Order fractions

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).

1. K.1
Add and subtract fractions with like denominators using number lines
2. K.2
Add and subtract fractions with like denominators

Add and subtract fractions with like denominators: word problems

Inequalities with addition and subtraction of like fractions

Add and subtract mixed numbers with like denominators

Add and subtract mixed numbers with like denominators: word problems

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.

Fractions of a number: word problems

Multiply unit fractions by whole numbers using number lines

Multiply unit fractions by whole numbers using models

Multiples of fractions

Multiply fractions by whole numbers using number lines

Multiply fractions by whole numbers using models

Multiply fractions by whole numbers I

Multiply fractions by whole numbers II

Estimate products of fractions and whole numbers

## Mixed operations Mixing different basic operations to solve questions and teaching the order of operations which tells us the order to solve steps in expressions with more than one operation.

Add, subtract, multiply or divide two whole numbers

Add, subtract, multiply or divide two whole numbers: word problems

Evaluate numerical expressions involving whole numbers

Add, subtract, multiply or divide two decimals

Add, subtract, multiply or divide two decimals: word problems

Evaluate numerical expressions involving decimals

Add, subtract or multiply two fractions

Add, subtract or multiply two 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.

Compare rational numbers

Put rational numbers in order

## 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

Word problems with extra or missing information

Guess-and-check word problems

Distance/direction to starting point

Use logical reasoning to find the order

## Ratios and rates 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.)

Write a ratio

Write a ratio: word problems

Identify equivalent ratios

Write an equivalent ratio

Ratio tables

Unit rates and equivalent rates

Compare ratios: word problems

Do the ratios form a proportion?

Solve the proportion

Scale drawings: word problems

## 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 each other and to fractions

Compare percents and fractions: word problems

Percents of numbers and money amounts

Percents of numbers: word problems

Find what percent one number is of another

Find what percent one number is of another: 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.

Estimate metric measurements

Convert and compare metric units

Metric mixed units

Convert square and cubic units of length

Convert between cubic metres and litres

Compare temperatures above and below zero

## Money Teaching students about how to add and subtract money values and understanding the prices and rounding them up. It is an important practice for real life problems like understanding the prices and how money relates to real world.

Find the number of each type of coin

Add and subtract money amounts: word problems

Multiply money by whole numbers

Multiply money: word problems

Divide money amounts

Divide money amounts: 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.

Sale prices

Which is the better coupon?

Unit prices

Unit prices with fractions and decimals

Percents – calculate tax, tip, mark-up and more

Simple interest

## Time Time is the ongoing sequence of events taking place. The past, present and future. We can measure time using clocks. Time has different units like second, minutes, hours, days and so on.

Elapsed time

Time units

Find start and end times

Convert between 12-hour and 24-hour time

## 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.

Objects on a coordinate plane

Graph points on a coordinate plane

Coordinate planes as maps

Follow directions on a coordinate plane

## 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.

Write variable expressions

Write variable expressions: word problems

Evaluate variable expressions with whole numbers

Evaluate multi-variable expressions

Evaluate variable expressions with decimals

Identify terms and coefficients

Sort factors of expressions

Properties of multiplication

Solve for a variable using properties of multiplication

Identify equivalent 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.

Does x satisfy an equation?

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 with whole numbers

Solve one-step equations with decimals

Solve one-step equations: word problems

## 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 an 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

## 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

Measure angles

Types of angles

Estimate angle measurements

Classify triangles

Identify trapezoids

Find missing angles in triangles and quadrilaterals

Sums of angles in polygons

Name angles

Parts of a circle

## Symmetry and transformations When two or more parts are identical after a flip, slide or turn we say it has symmetry. The simplest symmetry is reflection symmetry, sometimes called line symmetry or mirror symmetry. Other types of symmetries are Rotational symmetry and point symmetry. When we change a shape by using Turn, flip, slide or resize it is called transformation.

Symmetry

Reflection, rotation and translation

Translations: graph the image

Reflections: graph the image

Rotations: graph the image

Similar and congruent figures

Find side lengths of similar figures

## 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”.

Identify polyhedra

Which figure is being described?

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 squares and rectangles

Area of triangles

Area of parallelograms and trapezoids

Area of compound figures

Area between two rectangles

Area and perimeter of figures on grids

Area and perimeter: word problems

Rectangles: relationship between perimeter and area

Compare area and perimeter of two figures

Volume of cubes and rectangular prisms

Surface area of cubes and rectangular prisms

Volume of triangular prisms

Surface area of triangular prisms

Relate volume and surface area

## Data and graphs A collection of facts, such as numbers, measurements or observations is called data. We can create a table with the data. A diagram of values, usually shown as lines is called graph.

Interpret pictographs

Create pictographs

Interpret stem-and-leaf plots

Create stem-and-leaf plots

Interpret line plots

Create line plots

Create frequency tables

Interpret bar graphs

Create bar graphs

Interpret double bar graphs

Create double bar graphs

Interpret histograms

Create histograms

Circle graphs with fractions

Interpret line graphs

Create line graphs

Interpret double line graphs

Create double line graphs

Choose the best type of graph

## 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

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).

Combinations

Probability of one event

Make predictions

Probability of opposite, mutually exclusive and overlapping events

Compound events – find the number of outcomes by counting