## CONTENTS The beginning of Junior School, Grade 4 is the year of sports and camps and more complex syllabus. As children transition to more definitive number sense and introductions to concepts including geometry, graphs, logical reasoning. ## 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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Word names for numbers
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Roman numerals
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Prime and composite numbers
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Rounding
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Even or odd: arithmetic rules
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Inequalities with number lines
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Put numbers up to four digits in order
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Compare numbers up to five digits 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).
Add numbers up to five digits
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Add numbers up to five digits: word problems
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Addition: fill in the missing digits
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Add three or more numbers up to five digits each
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Addition patterns over increasing place values
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Choose numbers with a particular sum
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Estimate sums
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Estimate sums: word problems

## Subtraction In the primary grades, students develop an understanding of part-whole concepts – they learn that two or more parts can be separated from a whole (Subtraction).
Subtract numbers up to five digits
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Subtract numbers up to five digits: word problems
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Subtraction: fill in the missing digits
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Subtraction patterns over increasing place values
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Choose numbers with a particular difference
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Estimate differences
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Estimate differences: word problems

## Multiplication The multiplication of numbers can be seen as repeated addition. For example, 3×4 = 4+4+4
Multiplication facts to 10
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Compare numbers using multiplication
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Choose the multiples of a given number up to 12
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Multiply 1-digit numbers by 2-digit numbers
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Multiply 1-digit numbers by 2-digit numbers: word problems
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Multiply 1-digit numbers by 3-digit numbers
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Multiply 1-digit numbers by larger numbers
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Multiplication patterns over increasing place values
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Properties of multiplication
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Estimate products – multiply by 1-digit numbers
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Estimate products – multiply by larger numbers
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Estimate products: word problems
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Box multiplication
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Lattice multiplication
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Choose numbers with a particular product
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Multiply numbers ending in zeroes
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Multiply numbers ending in zeroes: word problems
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Multiply three numbers
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Multiply three or more numbers: word problems
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Inequalities with multiplication

## 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.
Division facts to 10
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Division facts to 10: word problems
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Properties of division
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Divide larger numbers
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Divide larger numbers: word problems
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Complete the division table
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Interpret remainders
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Choose numbers with a particular quotient
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Divide numbers ending in zeroes
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Estimate quotients
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Estimate quotients: word problems
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Divisibility rules
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Divisibility rules: word problems
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Division patterns over increasing place values
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Inequalities with division

## 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.
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Addition, subtraction, multiplication and division word problems
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Estimate sums, differences, products and quotients: word problems
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Multi-step word problems
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Word problems with extra or missing information
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Solve word problems using guess-and-check
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Choose numbers with a particular sum, difference, product or quotient
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Mentally add and subtract numbers ending in zeroes
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Inequalities involving addition, subtraction, multiplication and division

## 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
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Write variable expressions: word problems
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Evaluate variable expressions
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Write variable equations to represent word problems
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Solve variable equations

## Functions A function related an input to an output. It works like a machine that takes something in (input) and at the end gives us something back (output). F(x) is the traditional way of expressing functions. Each function has three parts the Input, the Relationship and the Output.
Input/output tables with addition, subtraction, multiplication and division
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Complete a table for a two-variable relationship
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Write a two-variable equation
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Graph a two-variable relationship

## Logical reasoning Logical reasoning is the process of using rational, systemic steps based on mathematical procedures to find an answer about your problem.
Find two numbers based on sum and difference
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Find two numbers based on sum, difference, product and quotient
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Find the order

## 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
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Complete a repeating pattern
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Make a repeating pattern
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Find the next row in a growing pattern of shapes
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Complete an increasing number pattern
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Complete a geometric number pattern
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Number patterns: word problems
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Number patterns: 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
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Graph points on a coordinate plane
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Follow directions on a coordinate plane
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Coordinate planes as maps

## 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.
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Interpret line graphs
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Create line graphs
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Interpret bar graphs
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Create bar graphs
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Interpret line plots
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Create line plots
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Frequency charts
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Interpret stem-and-leaf plots
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Create stem-and-leaf plots
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Circle graphs
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Choose the best type of graph

## 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.

Compare money amounts

Round money amounts

Making change

Price lists

## 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

## 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.

Match clocks and times

Match analogue and digital clocks

Convert time units

Add and subtract mixed time units

Fractions of time units

Elapsed time

Find start and end times: multi-step word problems
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Convert between 12-hour and 24-hour time

Time zones – 12-hour time

Time zones – 24-hour time

Transportation schedules – 12-hour time

Transportation schedules – 24-hour time

Time patterns

## Geometry Geometry is branch of mathematics which deals with shapes, lines and space. Two-dimensional geometry or plane geometry is about flat shapes like triangles and circles. Three-dimensional geometry is about solid shapes like spheres or cubes.

Which two-dimensional figure is being described?

Identify three-dimensional figures

Count vertices, edges and faces

Identify faces of three-dimensional figures

Which three-dimensional figure is being described?

Nets of three-dimensional figures

Is it a polygon?

Number of sides in polygons

Lines, line segments and rays

Parallel, perpendicular and intersecting lines

Acute, right, obtuse and straight angles

Types of triangles

Identify parallelograms

Identify trapezoids

Identify rectangles

Identify rhombuses

Identify congruent figures

Identify lines of symmetry

Rotational symmetry

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

Perimeter

Perimeter: find the missing side lengths

Find the area of figures made of unit squares

Select figures with a given area

Select two figures with the same area

Create figures with a given area

Find the area or missing side length of a rectangle

Area and perimeter: word problems

Volume

## Understand fractions Fractions help us to understand how many equal parts of a whole we have.

Understand fractions: fraction bars

Understand fractions: area models

Match fractions to models

Show fractions: fraction bars

Show fractions: area models

Unit fractions: modelling word problems

Unit fractions: word problems

Fractions of a whole: modelling word problems

Fractions of a whole: word problems

Fractions of a group: word problems

## Equivalent fractions Equivalent fractions are those fractions which have the same value even though they might look different at first glance.

Find equivalent fractions using area models

Graph equivalent fractions on number lines

Equivalent fractions

Fractions with denominators of 10, 100 and 1000

Patterns of equivalent fractions

Write fractions in lowest terms

## Compare and order fractions Comparing and deciding which fraction is greater or smaller than the other fractions.

Compare fractions with like numerators or denominators using models

Compare fractions with like numerators or denominators

Compare fractions using models

Graph and compare fractions on number lines

Benchmark fractions

Compare fractions using benchmarks

Compare fractions

Compare fractions in recipes

Order fractions with like numerators or denominators

Order fractions

Find smaller or larger fractions

## 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

Equivalent decimals

Graph decimals on number lines

Decimal number lines

Graph fractions as decimals on number lines

Convert fractions to decimals

Convert decimals to fractions

Convert decimals between standard and expanded form using fractions

Round decimals

Compare decimals on number lines

Compare decimal numbers

Put decimal numbers in order I

Compare decimals and fractions on number lines

Compare decimals and fractions

Put decimal numbers in order II

Number sequences involving decimals When we write numbers, the position of each digit is important. To learn how to add and subtract decimal numbers you need to learn about the position of digits and line up the decimal points.

Subtract decimal numbers

Add and subtract decimals: word problems

Choose decimals with a particular sum or difference

Add three or more decimals: word problems

Complete the addition or subtraction sentence 