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NA5-6: Know and apply standard form, significant figures, rounding, and decimal place value.

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Elaboration on this Achievement Objective

This means students will be able to express a given whole number or decimal measurements in standard form and vice versa and understand the potential rounding that may be involved. Standard form (scientific notation) at this level should involve integral exponents, for example 24 300 = 2.43 x 104 or 0.0243 = 2.43 x 10-2. This understanding of decimal place value and rounding should include interpretation of the potential value of a measurement when it is expressed using significant figures, for example 2.3m (2sf.) has a potential measurement of 2. 25≤m<2.35 whereas 2.300 (4sf.) has a potential measurement of 2.295≤m<2.305. Students should also apply decimal place value and sensible rounding through estimating in a way that is suitable to the context, and recognising the effects of that rounding on the accuracy of the estimation, for example 48.7 ÷ 2.13 = ? can be estimated by 50 ÷ 2 = 25 but the rounding results in an estimate that is too high. This does not include putting error bounds on estimations.

 

Teaching resources for this Achievement Objective
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Astronomical Proportions

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.

solve problems involving ratios

use rounding to solve proportion problems

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Bridging the Gaps

Level Five
Number and Algebra
Rich learning activities
The purpose of this activity is to engage students in using their knowledge of place value, standard form and rounding, to solve a problem involving a range of orders of magnitude.
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How many pieces? (years 7-10)

Level Four
Level Five
Integrated
This counting collections activity engages students in identifying which roll of toilet paper is better value.
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Learning from the past

Level Five
Integrated
Rich learning activities
The purpose of this activity is to engage students in solving a measurement problem.
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Line Up

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.

use rounding to multiply decimals

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No Space to Spare

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.

use a calculator to solve ratio problems

use rouding to solve proportion problems

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Rounding Numbers

Level Five
Number and Algebra
Units of Work
In this unit students will identify why it is important to round numbers sensibly. They will practise accurately and sensibly rounding in a range of different contexts.
  • Sensibly round whole numbers in context.
  • Sensibly round decimal numbers.
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Sunburst

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.

convert between standard and normal form

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The World's Rice Bowl

Level Five
Number and Algebra
The purpose of this unit is to engage students, in an integrated mathematics/social sciences context, in applying their understanding of place value and standard form to investigate a problem of global resources. Students also develop their skills and knowledge on the Multiplicative Thinking...
  • Express large numbers in standard form.
  • Apply rates measurements in different scales to problem solving.
  • Find and use specified rates in a problem solving context.
  • Find and use a fraction or rate from values expressed in standard form. 
  • Display large numbers on a graph with a suitable scale in a given300
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Working backwards

Level Five
Number and Algebra
Problem solving activities
This problem solving activity has a number focus.
  • Use their mathematical knowledge to invent problems.
  • Devise and use problem solving strategies to explore situations mathematically.