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Home
Year 5
Problem solving

Year 5

1. Number and Algebra

1.1. Number & place value

1.1.1. Words problems on estimate products

1.1.2. LCM (Lowest Common Multiple)

1.1.3. HCF (Highest Common Factor)

1.1.4. Divisibility rules

1.1.5. Prime Factorisation

1.1.6. Prime & composite numbers

1.1.7. Division

1.1.7.1. Divide two-digit numbers by one-digit numbers using arrays

1.1.7.2. Divide three-digit numbers by one-digit numbers using area models

1.1.7.3. Divide by one-digit numbers

1.1.7.4. Divide by two-digit numbers

1.1.7.5. Divide using partial quotients

1.1.7.6. Interpreting remainders

1.1.7.7. Estimate quotients

1.1.7.8. Words problems on estimate quotients

1.1.9. Word problems on multiplication of one-digit number

1.1.10. Word problems on multiplication of two-digit numbers

1.1.11. Multiply a two-digit number by a larger number

1.1.12. Multiply two-digit numbers by two-digit numbers using area models II

1.1.13. Multiply two-digit numbers by two-digit numbers using area models I

1.1.14. Multiply a two-digit number by a two-digit number

1.1.15. Multiply two-digit numbers by two-digit numbers using partial products

1.1.16. Estimate products

1.1.17. Place Value

1.1.18. Multiply one-digit numbers by multi-digit numbers using partial products

1.1.19. Multiply one-digit numbers by three-digit or four-digit numbers using expanded form

1.1.20. Multiply one-digit numbers by three-digit or four-digit numbers using area models I

1.1.21. Multiply one-digit numbers by three-digit or four-digit numbers using area models II

1.1.22. Even and odd: Properties

1.1.23. Rounding numbers

1.1.23.1. Rounding Off to the Nearest Ten

1.1.23.2. Rounding Off to the Nearest Hundred

1.1.23.3. Rounding Off to the Nearest Thousand

1.1.23.4. Rounding off to the Nearest Ten Thousand

1.1.24. Number conversion

1.1.25. Forming numbers

1.1.26. Write Number Names as Numerals

1.1.27. Write Numerals as Number Names

1.1.28. Compare Numbers

1.1.29. Numbers in Expanded form

1.1.30. Multiply by one-digit numbers

1.2. Operations on Large Numbers

1.2.1. Addition of Numbers

1.2.2. Subtraction of Numbers

1.2.3. Division of Large Numbers

1.2.4. Word Problem on Operations on Large Numbers

1.2.4.1. Word Problem on Addition of Numbers

1.2.4.2. Word Problem on Subtraction of Numbers

1.2.4.3. Word Problem on Multiplication

1.2.4.4. Word Problem on Division

2. Factors and Multiples

2.1. Factors and Multiples of a Number

2.1.1. Finding Factors of a Number

2.1.2. Finding Multiples of a Number

2.1.3. Word Problems on Factors and Multiples

2.1.4. Properties of Factors and Multiples

2.1.5. Types of Numbers

2.1.5.1. Odd and Even Numbers

2.1.5.1.1. Even numbers

2.1.5.1.2. Odd numbers

2.1.5.1.3. Properties of Odd and Even numbers

2.1.5.2. Prime and Composite Numbers

2.1.5.2.1. Definition

2.1.5.2.2. Composite Numbers

2.1.5.2.3. Prime Numbers

2.1.5.2.4. Properties of Composite and Prime

2.1.5.3. Twin Primes

2.1.5.4. Co-Primes

2.2. Tests of Divisibility

2.2.1. Test Divisibility by 2

2.2.2. Test Divisibility by 3

2.2.3. Test Divisibility by 4

2.2.4. Test Divisibility by 5

2.2.5. Test Divisibility by 6

2.2.6. Test Divisibility by 7

2.2.7. Test Divisibility by 8

2.2.8. Test Divisibility by 9

2.2.9. Test Divisibility by 10

2.2.10. Test Divisibility by 11

2.3. Prime Factors of a Number

2.3.1. By Hit and Trial Method

2.3.2. By Factor Tree Method

2.3.3. By Prime Factorization

2.4. HCF and LCM

2.4.1. HCF (Highest Common Factor)

2.4.2. LCM (Lowest Common Multiple)

2.4.3. Properties of LCM and HCF

2.4.4. Word Problems on HCF and LCM

3. Fractions and decimals

3.1. Unit fractions on number lines

3.2. Inequalities with addition and subtraction of fractions

3.3. Add three or more fractions

3.4. Add and subtract mixed numbers with like denominators

3.5. Decompose fractions multiple ways

3.6. Decompose fractions

3.7. Compare unit fractions using number lines

3.8. Compare unit fractions using models

3.9. Compare unit fractions

3.10. Like and Unlike Fractions

3.11. Unit Fraction

3.12. Proper, Improper and Mixed Fractions

3.12.1. Understand the Meaning of Proper, Improper and Mixed Fractions

3.12.2. Convert Improper Fractions to Mixed Fractions

3.12.3. Convert Mixed Fractions to Improper Fractions

3.13. Equivalent Fractions

3.14. Simplest Form of a Fraction

3.15. Compare Fractions

3.15.1. Compare Fractions with Like Denominators

3.15.2. Compare Fractions with Like Numerators

3.15.3. Compare Fractions with Unlike Denominators and Unlike Numerators

3.16. Addition and Subtraction of Fractions

3.16.1. Addition of Fractions

3.16.1.1. Add fractions with like denominators using number lines

3.16.1.2. Addition of Like Fractions

3.16.2. Subtraction of Fractions

3.16.2.1. Subtract fractions with like denominators using number lines

3.16.2.2. Subtraction of Like Fractions

3.16.3. Simplify Expressions Involving Addition and Subtraction

3.17. Word Problems on Fractions

3.17.1. Word Problems on Forming Fractions

3.17.2. Word Problems on Addition and Subtraction of Fractions

4. Decimals

4.1. Decimals on number lines

4.2. Compare decimals and fractions

4.3. Compare decimals and fractions on number lines

4.4. Put assorted decimals, fractions and mixed numbers in order

4.5. Reading a Decimal Number

4.6. Place Value Chart

4.7. Pictorial Representation of a Decimal Number

4.8. Expanded Form of Decimal Numbers

4.9. Like and Unlike Decimals

4.10. Comparing Decimals

4.11. Ordering Decimals

4.12. Relate Decimals and Fractions

4.12.1. Convert Decimals to Fractions

4.12.1.1. Convert Decimals to Proper Fractions

4.12.1.2. Convert Decimals to Improper Fractions

4.12.1.3. Convert Decimals to Mixed Fractions

4.12.2. Convert Fractions to Decimals

4.12.2.1. Convert Fractions with Denominators as Powers of 10 to Decimals

4.12.2.2. Convert Any Fractions to Decimals

4.13. Operations on Decimals

4.13.1. Addition and Subtraction of Decimals

4.13.1.1. Words problems on addition of decimals

4.13.1.2. Words problems on subtraction of decimals

4.13.1.3. Addition of Decimals

4.13.1.4. Subtraction of Decimals

4.13.1.5. Mixed Operations on Decimals: Addition and Subtraction

4.14. Multiplication and Division of Decimals

4.14.1. Multiplication of Decimals

4.14.1.1. Multiplying a Decimal by 10, 100, 1000 etc

4.14.1.2. Multiplying a Decimal by a Whole Number

4.14.1.3. Multiplication of Two/Three Decimals

4.14.2. Division of Decimals

4.14.2.1. Division of a Decimal by 10, 100, 1000 etc

4.14.2.2. Division of a Decimal by a Multiple of 10, 100, 1000 etc

4.14.2.3. Division of a Decimal by a Whole Number

4.14.2.4. Division of a Decimal by a Decimal

4.14.2.5. Division of a Whole Number by a Decimal

4.14.3. Word Problems on Multiplication and Division of Decimals

4.14.4. Word problems on Mixed Operations on Decimals

5. Rounding Numbers

5.1. Rounding Off Numbers

5.1.1. Rounding Off to the Nearest Ten

5.1.2. Rounding Off to the Nearest Hundred

5.1.3. Rounding Off to the Nearest Thousand

5.1.4. Rounding off to the Nearest Ten Thousand

5.1.5. Rounding Off to the Nearest Hundred Thousand

5.1.6. Rounding Off to the Nearest Million

5.2. Rounding Off the Decimals

5.2.1. Rounding Off to the Nearest One

5.2.2. Rounding Off to the Nearest Tenth

5.2.3. Rounding Off to the Nearest Hundredth

5.2.4. Rounding Off to the Nearest Thousandth

6. Measurement and geometry

6.1. Measurement of Length

6.1.1. Conversion of Metric Units of Length

6.1.1.1. Conversion from Higher to Lower Units of Length

6.1.1.2. Conversion from Lower to Higher Units of Length

6.1.2. Addition and Subtraction of Lengths

6.1.2.1. Addition of Lengths

6.1.2.1.1. Addition of Lengths Given in Meters and Centimeters

6.1.2.1.2. Addition of Lengths Given in Kilometers and Meters

6.1.2.2. Subtraction of Lengths

6.1.2.2.1. Subtraction of Lengths Given in Meters and Centimeters

6.1.2.2.2. Subtraction of Lengths Given in Kilometers and Meters

6.1.3. Multiplication and Division of Lengths Measure

6.1.3.1. Multiplication of Lengths

6.1.3.2. Division of Lengths

6.1.4. Word Problems on Length

6.1.4.1. Word Problems on Addition and Subtraction of Lengths

6.1.4.2. Word Problems on Multiplication and Division of Lengths

6.2. Measurement of Weight

6.2.1. Conversion of Metric Units of Weight

6.2.1.1. Conversion from Higher to Lower Units of Weight

6.2.1.2. Conversion from Lower to Higher Units of Weight

6.2.2. Addition and Subtraction of Weights

6.2.2.1. Addition of Weights

6.2.2.1.1. Addition of Weights in Grams and Milligrams

6.2.2.1.2. Addition of Weights in Kilograms and Grams

6.2.2.2. Subtraction of Weights

6.2.2.2.1. Subtraction of Weights in Grams and Milligrams

6.2.2.2.2. Subtraction of Weights in Kilograms and Grams

6.2.3. Multiplication and Division of Weights

6.2.3.1. Multiplication of Weights

6.2.3.2. Division of Weights

6.2.4. Word Problems on Weight

6.2.4.1. Word Problems on Addition and Subtraction of Weights

6.2.4.2. Word Problems on Multiplication and Division of Weights

6.3. Measurement of Capacity

6.3.1. Conversion of Metric Units of Capacity

6.3.1.1. Conversion from Higher to Lower Units of Capacity

6.3.1.2. Conversion from Lower to Higher Units of Capacity

6.3.2. Addition and Subtraction of Capacity

6.3.2.1. Addition of Capacity in Liters and Milliliters

6.3.2.2. Subtraction of Capacity in Liters and Milliliters

6.3.3. Multiplication and Division of Capacity

6.3.3.1. Multiplication of Capacity

6.3.3.2. Division of Capacity

6.3.4. Word Problems on Capacity

6.3.4.1. Word Problems on Addition and Subtraction of Capacity

6.3.4.2. Word Problems on Multiplication and Division of Capacity

7. Average

8. Percentage

8.1. Convert a Fraction into Percentage

8.2. Convert a Percentage into Fraction

8.3. Convert Decimal into Percentage

8.4. Convert Percentage into Decimal

8.5. Percentage of a Quantity

8.6. Word Problems on Percentage

9. Time

9.1. 24-Hour Clock Time

9.1.1. Understanding 24-Hour Clock Time

9.1.2. Conversion from 24-Hour Clock Time to 12-Hour Clock Time

9.1.3. Conversion from 12-Hour Clock Time to 24-Hour Clock Time

9.2. Use of 'AM' and 'PM'

9.3. Relate Year, Month, Week, Days, Hours, Minutes, and Seconds

9.4. Addition and Subtraction of Time

9.4.1. Addition of Time

9.4.2. Subtraction of Time

9.4.3. Word Problems on Time

10. Money and financial mathematics

10.1. Reading financial records

10.2. Keeping financial records

10.3. Budget

10.4. Addition and Subtraction of Money

10.4.1. Addition of Money

10.4.2. Subtraction of Money

10.5. Multiplication and Division of Money

10.5.1. Multiplication of Money

10.5.2. Division of Money

10.6. Word problems on Money

10.6.1. Word Problems on Addition and Subtraction of Money

10.6.2. Word Problems on Multiplication and Division of Money

10.6.3. Word Problems on Money Involving a Mixed Operations on Money

11. Geometry

11.1. Understand the Basic Terms in Geometry (Point, Line, line segment, ray, and Plane)

11.2. Angles

11.2.1. Introduction to Angles

11.2.2. Interior And Exterior Of An Angle

11.2.3. Finding the Number of Angles in the Given Figure

11.2.4. Types of an Angle

11.2.5. Measuring an Angle by a Protractor

11.2.6. Complementary and Supplementary Angles

11.3. Types of Lines

11.3.1. Parallel Lines

11.3.2. Perpendicular Lines

11.3.3. Intersecting Lines

11.3.4. Identifying the Type of Line

11.4. Set Squares

11.5. Collinear and Non-Collinear Points

11.6. Triangles

11.6.1. Introduction to Triangles

11.6.2. Various Types of Triangles by Considering the Lengths of their Sides

11.6.3. Various Types of Triangles by Considering their Angles

11.6.4. The Possibility of Forming a Triangle with Sides of Given Lengths

11.6.5. Angle Sum Property of a Triangle

11.7. Circle

11.7.1. Terms Related to a Circle

11.7.2. Relationship Between Radius and Diameter of a Circle

11.7.3. Interior and Exterior of a Circle

11.7.4. Concentric Circles

12. Area and Perimeter

12.1. Understanding the Concept of Perimeter

12.2. Perimeter of a Triangle

12.3. Perimeter of Polygons

12.4. Area and Perimeter of a Square

12.5. Area and Perimeter of a Rectangle

12.6. Circumference of a Circle

13. Volume

13.1. Volume of Cuboid

13.2. Volume of Cube

13.3. Word Problems on Volume of Cube and Cuboid

14. Data Handling

14.1. Pictographs

14.1.1. Introduction to Pictograph

14.1.2. Drawing Pictographs

14.1.3. Interpreting Pictographs

14.2. Bar Graphs

14.2.1. Drawing Bar Graphs

14.2.2. Interpreting Bar Graphs

14.3. Pie Charts

15. Exponents

15.1. Understanding powers of ten

15.2. Write powers of ten with exponents

15.3. Multiply a whole number by a power of ten

15.4. Multiply a decimal by a power of ten

15.5. Divide by a power of ten

15.6. Understanding exponents

15.7. Evaluate exponents

15.8. Find the missing exponents

16. Problem solving

16.1. Make the largest and smallest possible quotient

16.2. Word Problems

16.2.1. Write appropriate numerical expressions

16.2.2. Multi-step word problems

16.2.2.1. Simple multi-step problems

16.2.2.2. Multi-step word problems involving remainders

16.2.2.3. Multi-step word problems: identify reasonable answers

16.2.2.4. Miscellaneous problems

16.3. Use Venn diagrams to solve problems

17. Pattern & Algebra

17.1. Arithmetic sequences with decimals

17.3. Arithmetic sequences with fractions

17.4. Complete the number pattern

17.5. Number sequence: word problems

18. Coordinate plane

18.1. Definition of coordinate plane

18.2. Find the coordinates

18.3. Graph points on a coordinate plane

18.4. Complete the table and draw the graph

18.5. Analyze graphed relationships

18.6. Miscellaneous problems

19. Variable expressions

19.1. Write variable expressions

19.2. Evaluate variable expressions

19.3. Write variable expressions: word problems

19.4. Solve the equations

19.4.1. With whole numbers

19.4.2. With decimals

19.5. Questions on two-variables equations

19.6. Questions on graph

19.7. Graph a two-variable relationship

19.8. Write a two-variable equation

19.9. Write variable equations: word problems

20. Probability and statistics

20.1. Revisiting concepts

20.2. Find the missing numbers

20.2.1. Mode

20.2.2. Mean

20.2.3. Median

20.2.4. Range

20.3. Interpret charts and graphs

20.3.1. For mode

20.3.2. For mean

20.3.3. For median

20.4. Understanding probability

20.5. Predictions

20.6. Combinations

21. Symmetry and transformations

21.1. Line symmetry

21.2. Rotational symmetry

21.3. Reflection, rotation, and translation

21.4. Identify congruent and similar figures

22. Two-dimensional figures

22.1. Revisiting concepts

22.2. Types of polygons

22.3. Lines and its type

22.4. Various angles

22.5. Measure angles with a protractor

22.6. Properties of polygons

22.7. Venn diagrams

22.8. Parts of a circle

23. Three-dimensional figures

23.1. Revisiting concepts

23.2. Nets of three-dimensional figures

23.3. Three-dimensional figures viewed from different perspectives

Year 5 Australian School Math Problem solving

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