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Problem Solving Steps - Student Reference Cards
3 4 5 6 Pre & Primary Essentials Resources Worksheets Mathematics Number & Place Value Patterns & Algebras 1 Page

Problem Solving Steps - Student Reference Cards

These student bookmarks have been designed as a reference for students when problem solving. This resource allows students to refer to the five problem solving steps that have been adapted from the Newman’s Analysis concept. Colour and black and white versions have been included, with four bookmarks per page. While these were predominately created as part of the Year 3 Problem Solving unit, they are a useful tool for any class working on problem solving. 
 

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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 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.
  • We are learning to solve problems involving division using different strategies and express answers as a whole number, decimal or fraction.
  • We are learning to solve problems involving division by a one digit number, including those that result in remainders.
  • We are learning to solve practical problems involving addition and multiplication and choosing operations and efficient calculation strategies to solve the problem.
  • We are learning to use efficient mental and written strategies and calculators to solve problems.
  • We are learning to solve practical problems involving natural and rational numbers and percentages in financial contexts.
  • We are learning to select and apply efficient mental and written strategies and digital technologies to solve problems involving addition, subtraction, multiplication and division with whole numbers.

Curriculum alignment

AC9M6N09 9 Use mathematical modelling to solve practical problems, involving rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made 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 AC9M3N07 9 Follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns 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 AC9M5N09 9 Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and 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 AC9M4A01 9 Find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations AC9M5N07 9 Solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction 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 ACMNA083 8.4 Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction ACMNA082 8.4 Solve word problems by using number sentences involving multiplication or division where there is no remainder ACMNA055 8.4 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation ACMNA057 8.4 Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies ACMNA060 8.4 Describe, continue, and create number patterns resulting from performing addition or subtraction ACMNA123 8.4 Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers ACMNA075 8.4 Recall multiplication facts up to 10 × 10 and related division facts ACMNA291 8.4 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems ACMNA101 8.4 Solve problems involving division by a one digit number, including those that result in a remainder
MA3-1WM old Describes and represents mathematical situations in a variety of ways using mathematical terminology and some conventions MA2-8NA old Generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values MA2-6NA old Uses mental and informal written strategies for multiplication and division MA2-5NA old Uses mental and written strategies for addition and subtraction involving two-, three-, four- and five-digit numbers MA2-3WM old Checks the accuracy of a statement and explains the reasoning used MA2-2WM old Selects and uses appropriate mental or written strategies, or technology, to solve problems MA2-1WM old Uses appropriate terminology to describe, and symbols to represent, mathematical ideas MA3-5NA old Selects and applies appropriate strategies for addition and subtraction with counting numbers of any size MA3-6NA old Selects and applies appropriate strategies for multiplication and division, and applies the order of operations to calculations involving more than one operation MA3-3WM old Gives a valid reason for supporting one possible solution over another MA3-2WM old Selects and applies appropriate problem- solving strategies, including the use of digital technologies, in undertaking investigations MA1-4NA old Applies place value, informally, to count, order, read and represent two- and three-digit numbers MA1-3WM old Supports conclusions by explaining or demonstrating how answers were obtained MA1-2WM old Uses objects, diagrams and technology to explore mathematical problems MA1-1WM old Describes mathematical situations and methods using everyday and some mathematical language, actions, materials, diagrams and symbols 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 MA2-AR-01 new Selects and uses mental and written strategies for addition and subtraction involving 2- and 3-digit numbers MA3-RN-02 new Compares and orders decimals up to 3 decimal places 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) MA3-RN-01 new Applies an understanding of place value and the role of zero to represent the properties of numbers MA1-CSQ-01 new Uses number bonds and the relationship between addition and subtraction to solve problems involving partitioning MA3-RN-03 new Determines percentages of quantities, and finds equivalent fractions and decimals for benchmark percentage values MA3-AR-01 new Selects and applies appropriate strategies to solve addition and subtraction problems MA3-MR-01 new Selects and applies appropriate strategies to solve multiplication and division problems MA3-MR-02 new Constructs and completes number sentences involving multiplicative relations, applying the order of operations to calculations MA3-RQF-01 new Compares and orders fractions with denominators of 2, 3, 4, 5, 6, 8 and 10 MA3-RQF-02 new Determines 1/2, 1/4, 1/5 and 1/10 of measures and quantities
VCMNA164 Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions VCMNA162 Solve word problems by using number sentences involving multiplication or division where there is no remainder 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 VCMNA156 Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder VCMNA133 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation VCMNA184 Solve problems involving division by a one digit number, including those that result in a remainder VCMNA163 Use equivalent number sentences involving addition and subtraction to find unknown quantities VCMNA135 Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies VCMNA138 Describe, continue, and create number patterns resulting from performing addition or subtraction VCMNA139 Use a function machine and the inverse machine as a model to apply mathematical rules to numbers or shapes VCMNA185 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems VCMNA191 Create simple financial plans VCMNA155 Recall multiplication facts up to 10 × 10 and related division facts VCMNA209 Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations VCMNA160 Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies

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

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