Module 1 Number

System

Module Content Lesson Resources Lesson Plans Exam Questions Probing Questions

Number System - Teacher Notes

Solvemymaths has produced pages like this for lots of topics

NRICH Tasks

NRICH: Sea Level
NRICH: Tug Harder!
NRICH
: Repetitiously
NRICH: Tiny Nines

      Extras
Superheroes
Real Time Statistics
Size of Universe
Animation
Video Worked Examples:
Surds 1  Simplifying surds
Surds 2  Multiplying surds
Surds 3  Rationalising surds
Surds 4  Rationalising surd

 

Place Value

This is an excellent visual which encourage students to estimate a point on a number line such as 3.7 then has the option of numbers such as 3.46 and then gives the solution by zooming in Click here

Rounding

Shopping Bills

Project a series of numbers on the board and ask them to do a running total, whilst keeping an accurate answer yourself using a calculator

Estimating shopping bills by rounding to the nearest whole number and pairing to make multiples of 10 give out till receipts with total missing and circulate to see what answers they get.

Reasoned Rounding
The first player rolls a 0-9 die twice and chooses which two-digit number they would like to make from the numbers rolled.  They then have to round this to the nearest value of 10, find the matching circle on the recording sheet and write their two digit number in one of the spaces ... -
Click here

Reasoned Rounding to the nearest hundred recording sheet (PDF version)
Reasoned Rounding to the nearest whole number 
recording sheet (PDF version)
Reasoned Rounding to the nearest tenth 
recording sheet (PDF version)

Round the Dice Decimals
There are three dice, each of them with faces labelled from 1 to 6.
When the dice are rolled they can be combined in six different ways to make a number less than 10 with two decimal places.

Can each of the six numbers round to the same whole number?
Can each of the six numbers round to a different whole number? -
Click here

 

Ordering Decimals

Write down a series of 6 decimal numbers on the board and ask pupils to rank them in order 1-6 from smallest to largest. - include a clear explanation of their reason.   Use this as an opportunity to link with the topic of rounding:

So                         0.437,          0.47,            0.5012,        0.52,            0.509
Round to 1dp          0.4,              0.5,              0.5,              0.5,              0.5
So Rank                
1
Round to 2 dp                           0.47,            0.50,                     0.52,            0.51
So Rank                                   
2            3            5            4

 

This method highlights the fact that the tenths are the most important value etc...

 

How could this be used?

 

FlashMaths: Rounding Numbers Click here

FlashMaths: Reading Scales Click here

 

Fractions    @solvemymaths    Click here

 

Ordering Fractions

Fractions on a Clothes Line Click here

Fraction Cards

Deal five cards to each player. Set the remainder of the deck face down in the middle of the table as a draw pile.

You will play six rounds:

       Closest to zero

       Closest to 1/4

       Closest to 1/3

       Closest to 1/2

       Closest to one

       Closest to two

In each round, players choose two cards from their hand to make a fraction that is as close as possible (but not equal) to the target number. Draw two cards to replenish your hand.

The player whose fraction is closest to the target collects all the cards played in that round. If there is a tie for closest fraction, the winners split the cards as evenly as they can, leaving any remaining cards on the table as a bonus for the winner of the next round.

After the last round, whoever has collected the most cards wins the game.

Ordering Fractions, Decimals and Percentages

SU N1:This is an excellent introductory exercise to assess the understanding of the pupils and involves matching cards which show Fractions, Decimals, Number Line, Percentage Shading - From Module 1 FDP resources folder - or Click here

 

Fractions   [Thanks to Jo @mathsjam  http://www.resourceaholic.com/]

Ordering fractions card game - Lets Play Math

Folding Fractions using a Square Piece of Paper Proof is Higher Tier

Using Lego

 

Fraction Talks   @NatBanting

The goal was to develop a simple visual that could foster creative thinking around fractions. An unassuming idea, and open disposition, began to open up huge spaces for mathematical action for my students.

 
The idea is simple, the medium is practical, and the thinking is rich. This site is a growing cache of materials designed for classroom teachers. Enjoy, invent, contribute - Click here
 

Multiply and Divide by Powers of 10

Start with the number line 1 to 9

x10 to and write the numbers above, x100 and write above again, /10 then /100 to get

100

200

300

400

500

600

700

800

900

10

20

30

40

50

60

70

80

90

1

2

3

4

5

6

7

8

9

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

From this we can deduce that 4.3 x 10 must lie between 40 and 50 and equals 43

This links to the work on standard form where we always begin with a number on the blue line.

We can also use it to reference problems like 34/10 = 3.4            320/100 etc...

Standard Form

Use this to draw out that you times by 10 each time you move up a row, and always start from the yellow row to give 600 = 6x10x10 = 6x102 and 0.009 = 9 and down 3 rows = 9x10-3  

 

Percentages

If the world were 100 people is a good introduction to percentages as it requires students to gather data about a wide range of information and then presenting in an appropriate way whilst giving them a secure understanding of the fact that a percentage is out of 100

   

 

This blog makes interesting reading - Click here
This site is a good starting point -
Click here
Finally try this one - Click here

Large Numbers   @itabn_andrew

Is that a Big Num8er? is a website that:

  • Puts numbers into a context we can understand.
  • Reduces big numbers to understandable comparisons.
  • Champions numeracy by writing about numbers and how they can describe, understand and control the world.
  • Lets you discover number facts, and share them.
  • Helps develop a Number Sense in an entertaining way - Click here
 

Recurring Decimals
[Thanks to Jo @mathsjam  http://www.resourceaholic.com/]

Repeating Decimals - Maths Assessment Project

Recurring Decimals Four in a Row - Teachit Maths

Recurring decimals activity and method - The Chalk Face

Bounds  [Thanks to Jo @mathsjam  http://www.resourceaholic.com/]

Upper and lower bounds questions - The Chalk Face

Painting bounds - The Chalk Face

Errors Student Sheet (& notes) - Nuffield Foundation

Surds Decimal Approximations

Angry Surds Game Click here 

 

Introducing Irrational Numbers

This document provides a good way of introducing the concept of irrational numbers through a combination of long multiplication, reasoning and proof - Click here

Visualising Irrational Numbers

Wheel of Theodorus - Method of Construction