NA5-2: Use prime numbers, common factors and multiples, and powers (including square roots).
Elaboration on this Achievement Objective
This means students will know that prime numbers are numbers divisible by only themselves and one, and apply this to the fundamental law of arithmetic that every counting number has a unique prime factorisation, for example 36 = 2 x 2 x 3 x 3 = 22 32. They should apply prime factorisation to problems that involve factors and multiples, including finding the least common multiple or highest common factor. For example, “What sized cuboids can be made using 105 unit cubes?”, or “What is 105 out of 231 in simplest form?”
They should understand and use the additive law of exponents, that is ab x ac = ab+c and a b ÷ ac = a b - c and compare powers relationally (without calculation) where this is appropriate, for example 36 >63 because (3x3)x(3x3)x(3x3)>6x6x6. Students should understand the arithmetic and geometric origin of square roots (for example, a square of area 144cm2 has a side length of 12cm) and use common square roots to estimate the value of other square roots. For example, √36 = 6 and √49 = 7 so √42 ≈ 6.5. They should also understand the convention for negative exponents through pattern. For example 21= 2 so 20= 1 so 2 -1= 1/2 since the effect of decreasing the exponent by one is to divide the previous power by two.
Teaching resources for this Achievement Objective
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Five
Number and Algebra
Units of Work
This unit uses a Babylonian clay tablet and the mathematics found on it as a catalyst to investigate a variety of mathematical ideas. This same catalyst is also used for the unit: Babylonian Mathematics 1. Areas under enlargement are discussed in the present unit, and lying behind the various...
Level Five
Number and Algebra
Units of Work
This unit uses a Babylonian clay tablet and the mathematics found on it as a catalyst to investigate a variety of mathematical ideas. This same catalyst is also used for the unit: Babylonian Mathematics 2. Areas under enlargement are discussed in the present unit, and lying behind the various...
Level Five
Number and Algebra
Secondary activities
These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see Related Resources) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10...
Level Five
Number and Algebra
Problem solving activities
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Four
Level Five
Number and Algebra
Units of Work
In this unit we are paying close attention to the general rule of a pattern for the first time. We look at odd and even numbers as well as multiples of small numbers. We also look at squares and cubes of numbers and see that it is possible to make more than one pattern from the same three initial...
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Three
Level Four
Level Five
Number and Algebra
This counting collections activity engages students in finding the number of squares of any size on a chessboard.
Level Five
Number and Algebra
Numeracy activities
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Five
Number and Algebra
Numeracy activities
Level Five
Number and Algebra
Problem solving activities
Level Five
Number and Algebra
Units of Work
This unit supports students in learning to solve a range of problems involving exponents.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Five
Number and Algebra
Numeracy activities
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Three
Level Five
Number and Algebra
Figure It Out activities
These are level 3 number and algebra and level 5 number problems from the Figure It Out series.A PDF of the student activity is included.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number activity from the Figure It Out series. It relates to Stage 8 of the Number Framework.A PDF of the student activity is included.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.
Level Five
Number and Algebra
Figure It Out activities
This is a level 5 number link activity from the Figure It Out series. It relates to Stage 8 of the Number Framework. A PDF of the student activity is included.