YEAR 5 MATHS FOCUS
NUMBERS AND ALGEBRA
Patterns & Algebra
Learning Experiences
Patterns & Algebra
PATTERNS & ALGEBRA
OUTCOME
A student:
MA3-8NA:
analyses and creates geometric and number patterns, constructs and completes number sentences, and locates points on the Cartesian plane
TEACHING POINTS | In Stage 3, students should be encouraged to use their own words to describe number patterns. Patterns can usually be described in more than one way and it is important for students to hear how other students describe the same pattern. Students’ descriptions of number patterns can then become more sophisticated as they experience a variety of ways of describing the same pattern. The teacher could begin to model the use of more appropriate mathematical language to encourage this development… |
| This substrand involves algebra without using letters to represent unknown values. When calculating unknown values, students need to be encouraged to work backwards and to describe the processes using inverse operations, rather than using trial-and-error methods. The inclusion of number sentences that do not have whole-number solutions will aid this process. | |
| To represent equality of mathematical expressions, the terms ‘is the same as’ and ‘is equal to’ should be used. Use of the word ‘equals’ may suggest that the right-hand side of an equation contains ‘the answer’, rather than a value equivalent to that on the left. |
| LANGUAGE | Students should be able to communicate using the following language: pattern, increase, decrease, missing number, number sentence, number line. |
Expectations of Attainment
Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (ACMNA107) | identify, continue and create simple number patterns involving addition and subtraction {Critical and creative thinking} |
| describe patterns using the terms ‘increase’ and ‘decrease’, eg for the pattern 48, 41, 34, 27, …, ‘The terms decrease by seven’ {Literacy} | |
| create, with materials or digital technologies, a variety of patterns using whole numbers, fractions or decimals, e.g. 1/4, 2/4, 3/4, 4/4, 5/4, 6/4, … or 2.2, 2.0, 1.8, 1.6, … {Information and communication technology capability, Critical and creative thinking} | |
| use a number line or other diagram to create patterns involving fractions or decimals |
Use equivalent number sentences involving multiplication and division to find unknown quantities (ACMNA121) | complete number sentences that involve more than one operation by calculating missing numbers, e.g. 5×□=4×10, 5×□=30−10 |
| – describe strategies for completing simple number sentences and justify solutions {Communicating, Reasoning, Critical and creative thinking} | |
| identify and use inverse operations to assist with the solution of number sentences, e.g. 125÷5=□ becomes □×5=125 | |
| – describe how inverse operations can be used to solve a number sentence {Communicating, Reasoning, Critical and creative thinking} | |
| complete number sentences involving multiplication and division, including those involving simple fractions or decimals, e.g. 7×□=7.7 | |
| – check solutions to number sentences by substituting the solution into the original question {Reasoning, Critical and creative thinking} | |
| write number sentences to match word problems that require finding a missing number, e.g. ‘I am thinking of a number that when I double it and add 5, the answer is 13. What is the number?’ {Literacy} |
Learning Experiences
To be added