Problem Solving Mat
This problem-solving mat can be printed in both colour and black and white. It could be printed and laminated for each student, to use multiple times. This supportive resource acts as a scaffold for students to support them through the five problem solving steps. This resource is part of the Problem-Solving unit plan, which was created predominately, for Year 3. However, this resource is fantastic for any grade focusing on problem solving.
Learning goals
- We are learning to use a range of mental strategies to solve simple addition and subtraction problems.
- We are learning to solve multiplication problems using mental and written strategies and calculators to check our answers.
- 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 × 10 and related division facts.
- 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 and identify equivalent number sentences involving addition and subtraction.
- We are learning to solve problems involving division by a one digit number, including those that result in remainders.
- We are learning to use efficient mental and written strategies and calculators to solve problems.
- 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.
- We are learning to recall addition facts to 20 and apply to related subtraction facts using a range of strategies.
- We are learning to solve problems involving modelling addition, subtraction, multiplication and division, using different strategies.
- We are learning to follow and create number sentences to investigate number patterns and rules and to find emerging patterns.
- 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 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 find unknown quantities in number sentences involving addition and subtraction, using the properties of numbers and operations.
- We are learning to recall multiplication facts up to 10 x 10 and related division facts, developing efficient mental strategies.
- 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 practical problems involving addition and multiplication and choosing operations and efficient calculation strategies to solve the problem.
- We are learning to solve practical problems involving natural and rational numbers and percentages in financial contexts.
Curriculum alignment
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
AC9M3N07
9
Follow and create algorithms involving a sequence of steps and decisions to investigate numbers; describe any emerging patterns
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
AC9M2A02
9
Recall and demonstrate proficiency with addition facts to 20; extend and apply facts to develop related subtraction facts
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
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
AC9M4A01
9
Find unknown values in numerical equations involving addition and subtraction, using the properties of numbers and operations
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
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
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
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
ACMNA057
8.4
Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies
ACMNA055
8.4
Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
ACMNA060
8.4
Describe, continue, and create number patterns resulting from performing addition or subtraction
ACMNA075
8.4
Recall multiplication facts up to 10 × 10 and related division facts
ACMNA082
8.4
Solve word problems by using number sentences involving multiplication or division where there is no remainder
ACMNA083
8.4
Find unknown quantities in number sentences involving addition and subtraction and identify equivalent number sentences involving addition and subtraction
ACMNA101
8.4
Solve problems involving division by a one digit number, including those that result in a remainder
ACMNA291
8.4
Use efficient mental and written strategies and apply appropriate digital technologies to solve problems
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
MA2-3WM
old
Checks the accuracy of a statement and explains the reasoning used
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
MA3-5NA
old
Selects and applies appropriate strategies for addition and subtraction with counting numbers of any size
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
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
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
MA2-1WM
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-MR-02
new
Completes number sentences involving multiplication and division by finding missing values
MA1-CSQ-01
new
Uses number bonds and the relationship between addition and subtraction to solve problems involving partitioning
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
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-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-RQF-02
new
Determines 1/2, 1/4, 1/5 and 1/10 of measures and quantities
MA3-RQF-01
new
Compares and orders fractions with denominators of 2, 3, 4, 5, 6, 8 and 10
MA3-MR-02
new
Constructs and completes number sentences involving multiplicative relations, applying the order of operations to calculations
MA3-MR-01
new
Selects and applies appropriate strategies to solve multiplication and division problems
MA3-AR-01
new
Selects and applies appropriate strategies to solve addition and subtraction problems
MA3-RN-03
new
Determines percentages of quantities, and finds equivalent fractions and decimals for benchmark percentage values
MA3-RN-02
new
Compares and orders decimals up to 3 decimal places
MA3-RN-01
new
Applies an understanding of place value and the role of zero to represent the properties of numbers
VCMNA135
Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies
VCMNA103
Investigate number sequences, initially those increasing and decreasing by twos, threes, fives and ten from any starting point, then moving to other sequences
VCMNA107
Solve simple addition and subtraction problems using a range of efficient mental and written strategies
VCMNA133
Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation
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
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
VCMNA155
Recall multiplication facts up to 10 × 10 and related division facts
VCMNA156
Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder
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
VCMNA163
Use equivalent number sentences involving addition and subtraction to find unknown quantities
VCMNA164
Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions
VCMNA184
Solve problems involving division by a one digit number, including those that result in a remainder
VCMNA185
Use efficient mental and written strategies and apply appropriate digital technologies to solve problems
VCMNA191
Create simple financial plans
Australian Curriculum covers QLD / SA / WA / NT / TAS / ACT.
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