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Problem Solving
3 4 Pre & Primary Essentials Worksheets Mathematics Number & Place Value Patterns & Algebras 1 Page

Problem Solving

This worksheet contains three problem solving questions which could be used as an explicit teaching activity, independent activity, during maths rotations or as a guided maths group. The worksheet provides space for students to show their working out by applying a problem-solving strategy. While this was predominately created as part of the Year 3 Problem Solving unit, it would also be a great activity for Year 4 students.

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Learning goals

  • We are learning to recall addition facts to 20 and apply to related subtraction facts using a range of strategies.
  • We are learning to recall addition and subtraction facts to 20 and to develop mental strategies for larger numbers.
  • We are learning to use a range of mental strategies to solve simple addition and subtraction problems.
  • We are learning to solve problems involving modelling addition, subtraction, multiplication and division, using different strategies.
  • We are learning to solve multiplication problems using mental and written strategies and calculators to check our answers.
  • We are learning to follow and create number sentences to investigate number patterns and rules and to find emerging patterns.
  • We are learning to describe, continue and create number patterns and use addition and subtraction to identify the rule.
  • We are learning to recognise and explain multiplying and dividing by 10 using place value charts, numeral expanders or sliders and to use a calculator to understand the relationship between the place value of digits when multiplying and dividing by 10.
  • We are learning to partition, rearrange and regroup numbers to at least tens of thousands using place value groupings.
  • We are learning to recall multiplication facts up to 10 x 10 and related division facts, developing efficient mental strategies.
  • We are learning to recall multiplication facts up to 10 × 10 and related division facts.
  • We are learning to use a range of strategies to solve addition, subtraction, multiplication and division where there is no remainder.
  • We are learning to solve practical problems involving addition and multiplication including money problems, such as budgeting, using multiple strategies.
  • We are learning to solve word problems by using number sentences involving multiplication or division where there is no remainder.
  • We are learning to find unknown quantities in number sentences involving addition and subtraction, using the properties of numbers and operations.
  • We are learning to find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction.

Curriculum alignment

AC9M3N07 9 Follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns AC9M2A02 9 Recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts AC9M3A02 9 Extend and apply knowledge of addition and subtraction facts to 20 to develop efficient mental strategies for computation with larger numbers without a calculator AC9M3N06 9 Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation AC9M4A01 9 Find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations AC9M4N08 9 Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems using number sentences and choose efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation AC9M4N06 9 Develop efficient strategies and use appropriate digital tools for solving problems involving addition and subtraction, and multiplication and division where there is no remainder AC9M4A02 9 Recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator AC9M4N05 9 Solve problems involving multiplying or dividing natural numbers by multiples and powers of 10 without a calculator, using the multiplicative relationship between the place value of digits ACMNA057 8.4 Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies ACMNA075 8.4 Recall multiplication facts up to 10 × 10 and related division facts ACMNA060 8.4 Describe, continue, and create number patterns resulting from performing addition or subtraction ACMNA082 8.4 Solve word problems by using number sentences involving multiplication or division where there is no remainder ACMNA073 8.4 Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems ACMNA055 8.4 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation ACMNA083 8.4 Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction
MA2-6NA old Uses mental and informal written strategies for multiplication and division MA1-1WM old Describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols MA1-2WM old Uses objects, diagrams and technology to explore mathematical problems MA1-3WM old Supports conclusions by explaining or demonstrating how answers were obtained MA1-4NA old Applies place value, informally, to count, order, read and represent two- and three-digit numbers MA2-8NA old Generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values MA2-5NA old Uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers MA2-1WM old Uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA2-2WM old Selects and uses appropriate mental or written strategies, or technology, to solve problems MA2-3WM old Checks the accuracy of a statement and explains the reasoning used MA2-AR-01 new Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers MA2-RN-01 new Applies an understanding of place value and the role of zero to represent numbers to at least tens of thousands MA2-RN-02 new Represents and compares decimals up to 2 decimal places using place value MA1-CSQ-01 new Uses number bonds and the relationship between addition and subtraction to solve problems involving partitioning MA2-AR-02 new Completes number sentences involving addition and subtraction by finding missing values MA2-MR-01 new Represents and uses the structure of multiplicative relations to 10 × 10 to solve problems MA2-MR-02 new Completes number sentences involving multiplication and division by finding missing values MA2-PF-01 new Represents and compares halves, quarters, thirds and fifths as lengths on a number line and their related fractions formed by halving (eighths, sixths and tenths)
VCMNA135 Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies VCMNA107 Solve simple addition and subtraction problems using a range of efficient mental and written strategies VCMNA103 Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences VCMNA138 Describe, continue, and create number patterns resulting from performing addition or subtraction VCMNA133 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation VCMNA139 Use a function machine and the inverse machine as a model to apply mathematical rules to numbers or shapes VCMNA164 Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions VCMNA163 Use equivalent number sentences involving addition and subtraction to find unknown quantities VCMNA160 Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies VCMNA162 Solve word problems by using number sentences involving multiplication or division where there is no remainder VCMNA156 Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder VCMNA155 Recall multiplication facts up to 10 × 10 and related division facts VCMNA153 Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems

Australian Curriculum covers QLD / SA / WA / NT / TAS / ACT.

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