## CONTENTS The exciting new year for every child, Grade 5 is one of the critical years of learning. This is also an important year from the perspective of concept absorption. From basic mathematics of addition, subtraction, multiplication, and division to more evolved concepts in decimals 5 elaborates on the applications of the basic concepts including the metric system, probability, fractions while introducing new facets of graphs. ## Place values and number sense In mathematics Number Sense refers to understanding of numbers, their relationship and how they are affected by the four basic operations. Number senses is important because it helps to develop useful strategies when counting, measuring or estimating.
Place values
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Convert between place values
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Compare numbers up to millions
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Word names for numbers
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Roman numerals
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Rounding
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Even or odd: arithmetic rules 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
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Add and subtract whole numbers: word problems
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Fill in the missing digits
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Choose numbers with a particular sum or difference
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Estimate sums and differences of whole numbers
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Estimate sums and differences: word problems

## 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 by one-digit numbers
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Multiply by one-digit numbers: word problems
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Multiplication patterns over increasing place values
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Multiply numbers ending in zeroes
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Multiply numbers ending in zeroes: word problems
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Properties of multiplication
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Choose numbers with a particular product
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Estimate products
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Estimate products: word problems
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Box multiplication
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Lattice multiplication
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Multiply by 2-digit numbers: complete the missing steps
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Multiply 2-digit numbers by 2-digit numbers
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Multiply by 2-digit numbers: word problems
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Multiply three or four numbers
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Multiply three or four numbers: word problems
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Multiply 3-digit by 2-digit numbers
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Multiply 3-digit by 2-digit numbers: word problems
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Inequalities with multiplication

## Division The sum or difference of terms which have variables raised to positive integer powers and which have coefficients. A polynomial can have constants, variables and exponents, but never division by variable. Even though the poly- means many the polynomials terms should be finite.

Division facts to 12

Division facts to 12: word problems

Divide by one-digit numbers

Divide by one-digit numbers: word problems

Divide by one-digit numbers: interpret remainders

Estimate quotients

Estimate quotients: word problems

Division patterns over increasing place values

Divide numbers ending in zeroes

Divide numbers ending in zeroes: word problems

Choose numbers with a particular quotient

Divide by two-digit numbers

Divide by two-digit numbers: word problems

## 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 and composite numbers

Prime factorization

Divisibility rules

Divisibility rules: word problems

Greatest common factor

Least common multiple

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

What decimal number is illustrated?

Model decimals and fractions

Understanding decimals expressed in words

Place values in decimal numbers

Convert decimals between standard and expanded form

Equivalent decimals

Round decimals

Decimal number lines

Compare decimals on number lines

Compare decimal numbers

Put decimal numbers in order

Convert fractions to decimals

Convert decimals to fractions

Convert decimals between standard and expanded form using fractions

Compare decimals and fractions on number lines

Compare decimals and fractions

Put assorted decimals, fractions and mixed numbers in order Adding and subtracting decimals is easy when you keep your work clean. It is like the normal addition and subtraction with one extra detail aka decimal point.

Add and subtract decimals: word problems

Choose decimals with a particular sum or difference

Complete the addition or subtraction sentence

Inequalities with decimal addition and subtraction

Estimate sums and differences of decimals

## 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.

Estimate products of decimals

Multiply a decimal by a power of ten

Multiply decimals and whole numbers

Multiply decimals and whole numbers: word problems

Inequalities with decimal multiplication

Divide by powers of ten

Decimal division patterns over increasing place values

## 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.

Add and subtract money: word problems

Multiply money amounts: word problems

Multiply money amounts with decimals: word problems

Divide money amounts with decimals: word problems

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

Show fractions: fraction bars

Show fractions: area models

Fractions review

Fractions of a whole: word problems

Fractions of a group: word problems

Mixed numbers

Fractions of a number

Fractions of a number: word problems

Arithmetic sequences with fractions

Geometric sequences with fractions

Round mixed numbers

## Fraction equivalence and ordering Equivalent fractions are those fractions which have the same value even though they might look different at first glance. Comparing and deciding which fraction is greater or smaller than the other fractions and ordering them.

Find equivalent fractions using area models

Graph equivalent fractions on number lines

Equivalent fractions

Patterns of equivalent fractions

Write fractions in lowest terms

Graph and compare fractions on number lines

Compare fractions

Compare fractions and mixed numbers

Order fractions with like denominators

Order fractions with like numerators

Order fractions 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).

Decompose fractions multiple ways

Add and subtract fractions with like denominators using number lines

Add and subtract fractions with like denominators

Add and subtract fractions with like denominators: word problems

Add and subtract mixed numbers with like denominators

Add and subtract mixed numbers with like denominators: word problems

Add up to 4 fractions with denominators of 10 and 100

Add three or more fractions: word problems

Complete addition and subtraction sentences with fractions

Inequalities with addition and subtraction of fractions

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

Multiples of fractions

Multiply unit fractions and whole numbers: sorting

Multiply fractions by whole numbers using number lines

Multiply fractions by whole numbers using models

Multiply fractions and whole numbers: sorting

Multiply fractions by whole numbers

Multiply fractions by whole numbers: input/output tables

## 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 and divide whole numbers

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

Write numerical expressions

Evaluate numerical expressions

Add, subtract, multiply and divide decimals

Add, subtract and multiply decimals: word problems

## Problem solving 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.

Multi-step word problems

Word problems with extra or missing information

Guess-and-check problems

Find the order

Use Venn diagrams to solve problems

Price lists

## Patterns and 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.

Find the next shape in a repeating pattern

Complete a repeating pattern

Make a repeating pattern

Find the next row in a growing pattern of shapes

Complete an increasing number sequence

Complete a geometric number sequence

Use a rule to complete a number sequence

Number sequences: word problems

Number sequences: mixed review

## 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

## Variable expressions A variable is a symbol that stands in for an unknown value, any symbol can be used to represent a variable. Variable expression is a combination of terms and mathematical operations that contains at least one variable.

Write variable expressions

Write variable expressions: word problems

Evaluate variable expressions

Write variable equations: word problems

Solve equations with whole numbers

Find a value using two-variable equations

Complete a table for a two-variable relationship

Complete a table from a graph

Graph a two-variable relationship

Write a two-variable equation

## 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 line graphs

Create line graphs

Interpret bar graphs

Create bar graphs

Interpret pictographs

Create pictographs

Interpret histograms

Create histograms

Interpret line plots

Create line plots

Frequency charts

Interpret stem-and-leaf plots

Create stem-and-leaf plots

Circle graphs

Choose the best type of graph

## Probability and statistics 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).

Calculate mean, median and mode

Mean, median and mode: find the missing number

Interpret charts to find mean, median and mode

Understanding probability

Find the probability

Make predictions

Combinations

## 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.

Convert time units

Add and subtract mixed time units

Elapsed time

Find start and end times: word problems

Convert between 12-hour and 24-hour time

Time zones – 12-hour time

Time zones – 24-hour time

Schedules and timelines – 12-hour time

Schedules – 24-hour time

Time patterns

## 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.

Choose the appropriate metric unit of measure

Compare and convert metric units of length

Compare and convert metric units of mass

Compare and convert metric units of volume

Choose the more reasonable temperature

## 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”.

Is it a polygon?

Number of sides in polygons

Regular and irregular polygons

Parallel, perpendicular and intersecting lines

Types of angles

Measure angles with a protractor

Classify triangles

Identify parallelograms

Identify trapezoids

Identify rectangles

Identify rhombuses

## 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.

Lines of symmetry

Rotational symmetry

Reflection, rotation and translation

Combinations of reflections, rotations, and translations

Transformations on the coordinate plane

Identify congruent and 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 three-dimensional figures

Count vertices, edges and faces

Nets of three-dimensional figures

Three-dimensional figures viewed from different perspectives

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

Perimeter with whole number side lengths

Perimeter with decimal side lengths

Area of squares and rectangles

Area and perimeter of figures on grids

Use area and perimeter to determine cost

Volume of rectangular prisms made of unit cubes

Volume of irregular figures made of unit cubes

Volume of cubes and rectangular prisms

Surface area