Using double number lines

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Using double number lines

• Sandra Cathcart
• The Power of 10
• NZAMT 2007

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What we going to look at to day?

• Where we use double number lines
• Using the teaching model
• Solving problems - part one
• Resources for practising and sustainability
• What do our students need to know to do this
  work?
• Solving problems - part two
• Solving problems - part three
• Other uses

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Where can we use double number lines?

• Some examples
• To solve problems
• To solve currency conversion problems
• To compare fractions
• Using proportion to make predictions
• For looking at comparisons

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Teaching progression

• Start by
• Using materials, diagrams to illustrate and solve
  the problem
• Progress to
• Developing mental images to help solve the
  problem
• Extend to
• Working abstractly with the number property

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Using double number lines to solve problems
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Percentages

• What do we expect to cover in years 9/10

• Finding one number as a of another
• Finding a of a quantity
• Finding the total given a of the total
• Increase/decrease by a
• Finding the original after an increase/decrease

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20 of 150 is 30

• 20 of 150 is
• 20 of is 30
• of 150 is 30

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Question (in context)
The local dairy farmer is selling 20 of his herd
of 150 cows. How many is he selling?
Rewrite
20 of 150 is ?
?
150
0 20
100
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How do we use the lines to get the answer?
150 divided by 5 30
20 x 5 100
Find 10 150 divided by 10
So 10 15 So 20 30
10
15 x 10
15 x 2
10 x 2
10 x 10
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There are 30 students in 9CT and 40 are girls.
How many girls are there in the class?
40 of 30 is ?
In a berry mix there are 30 strawberries and
20 raspberries and the rest are blackberries. In
a 500gm punnet of berries what weight are the
strawberries?
30 of 500gm is ?
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Abigail is working on a set of 50 number problems
and she has just finished question 28. What of
the questions has she finished.
28 is ? of 50
Mr Sharp spent the day at the races and his
horses were placed in 8 out of 20 races. In what
of the races was he successful?
8 is ? of 20
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30 of the swimming team are girls. If there are
18 girls . How many are in the team altogether?
18 is 30 of ?
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Moving to number properties
20 of 150 is ? Now is time to link what they
know about with decimal fractions. How else can
we write this? What does 20 actually mean? How
could we do this without the number line? For
some students this stage will be a long time
coming! For others they will tell you. Now might
be the time to bring in a calculator and some
more awkward qs
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Resources

• Starters
• FIO
• Activities - group
• - individual
• - class

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Activities to practice these skills

• Activity 1
• Activity 3
• Note these are not teaching activities

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Figure It Out

• Proportional Reasoning Book 2
• Fully grown Page 9
• The Percentage Game page 14/15
• Laser Blazer page 12/13

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What do students need to be able to do before we
use this?
Have a sound knowledge of percentage

• Recall of all multiplication and division facts

Discounts, markups, inflation etc

• To know answers must be in context with correct
  units

• Common factors and lowest common multiples

• AM/AP

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Revision of prior knowledge
What is prior knowledge? Some activities to use
to give students constant revision.
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Decreasing by a
Sarah went shopping for a new bike which cost
350 When she got to town there was a sale and
she got 20 off the price, What did she pay?
Did she pay more or less? How much less? So
instead of paying 100 she only paid? Show all
this on the number lines
350
0
80
100
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Increasing by a percentage
The value of a 400 antique vase has been
increased by 20. What is its value now? What
questions do we ask?
120 of 400 is ?
?
400
0
120
100
Or divide 400 by 10 (to get 10) and multiply by
12.
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Finding the original amount after a
increase/decrease
Example After an increase in his weekly wage of
20 Joe has 480.What was his wage before the
increase?
Talk through and write the maths question 480 is
120 of ?
Complete a number line with this information
480
?
0
100
120
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Activities to practice these skills
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