Yr 9 Unit 2 – Number – Higher

6 lessons

Rounding

Support Objectives / Grade / Ref
1 / Round a number to one significant figure.
AQA Higher 1 pages 20 – 21
FVT Rounding
Bbc.co.uk – rounding off / E / H2.3h
2 / Estimate answers to calculations involving multiplication and division.
AQA Higher pages 20 - 21 / D / H2.1d
Core Objectives / Grade / Ref
1 / Estimate answers to calculations involving multiplication and division by numbers less than one.
AQA Higher pages 21 - 22 / C / H2.3h
2 / Find minimum and maximum values.
AQA Higher 1 pages 23 – 24
FVT Lower and upper bounds
ET Lower and upper bounds / C / H2.4d
Extension Objectives / Grade / Ref
1 / Round to a given number of significant figures.
FVT Rounding
Bbc.co.uk – rounding off / B / H2.3p

Vocabulary

Round Decimal places Upper bound

Significant figure EstimateLower bound

..\Vocabulary\Year 9 Unit 2 Num.doc

Ideas for starters

*Ten students in the class are each given a card with a number between say, seven and eight, with different numbers of decimal places given (e.g. 7.5, 7.106, 7.21, etc.) They come out to the front one by one to form a number line with all the numbers in correct order whilst the rest of the class monitor the decisions and offer advice. Ask questions such as ‘tell me a number between 7.21 and 7.5’, ‘which number s are nearer to 7 than they are to 8?’Etc. Depending on the class, you may prefer the set of cards to be given to pairs or small groups of students to arrange in order of size rather than making it a front-of-the-class activity. In either case, it would be useful for students to mark the numbers on a number line.

*Students all have small whiteboards. Ask them to show for example, ‘three numbers between 5 and 6’.

*Practice rounding numbers of different sizes to one significant figure.

*Practice mental calculations such as 5x20, 80x2, and perhaps using small whiteboards to encourage full participation and to enable you to assess progress.

*Ask students to make a table of squares: 1x1=1

2x2=4 etc

as far as they can get in the time given. Quicker students can explore the number patterns in the table and build up the list of squares without having to do all the multiplications.

* Mental multiplications/division by 10 and 100.

*Starting from 5, go round the class adding 0.4, 0.35, …

*Starting from 20, go round the class subtracting 0.4, 0.35, …

*Estimating exercise: Estimate the length of the classroom, height of a chair, width of a door, length of a pencil, temperature off the classroom, mass of a chair, volume of the classroom etc.

*What number is halfway between 6 and 12? 7 and 10? 4.2 and 5? 4.2 and 4.7? 4.2 and 4.35?

* Split the class into two teams. Then write a sum on the board e.g. 14.3% of 89. Each team then has to estimate the answer to 1 d.p. If the team is spot on they get a hole-in-one and 10 points. If neither team gets it they get a second chance to earn 5 points for a birdie. The team with the most points wins.

HOLS/maths investigations

* AQA Higher I pages 22, 23, 24.

* Investigate real life suitable degrees of accuracy.

* Use a calculator to investigate what happens when numbers are multiplied and divided by numbers between 0 and 1.

ICT links / citizenship

* Kaleidos – Search Rounding (various)

* Kaleidos – Its Significant

Ideas for plenaries

* After some time to prepare, small groups of students give short presentations to the class explaining how to round numbers to the nearest 100, or how to estimate the answers to calculations. Alternatively, or in addition, they could go make a poster to explain the poster.

*Students make a large number line, showing on it, for example, which numbers round to 3.4, 3.5 etc.

* Students provide explanations of the term ‘significant figures’ and discuss which

explanations are the most helpful.

*Explain how you know that 2.9x1.7 is less than 6.

*How do you know that 6.1by 1.9 is bigger than 3?

*Find the minimum and maximum values for the number 40 rounded to the nearest…

What if 40 is a length or a weight? What if 40 is a mark or an age?

Ideas for homework

* AQA Foundation I Homework book. Chapter 4. Numbers 1, 2, 3,4.

* 9/Rounding and Estimating

* Learn tables up to 15 x 15.

* Create a poster and bring in examples from newspapers etc where numbers have been estimated and used in real life situations.

Webmaths Rounding

Webmaths Rounding 2

Webmaths Rounding and Estimation

Webmaths Comparing calculations and estimating

Webmaths Upper and Lower Bounds

Webmaths Calculations with Upper and Lower Bounds

Ideas for Formative Comments

* Always check the previous digit before rounding up. If it is less than 5 there is no change.

*Always round your answers to a suitable degree of accuracy.

* Check your answers carefully when multiplying and dividing by numbers between 0 and 1.