Exploring Decimal Fractions

1
Exploring Decimal Fractions

• Louise Addison
• Pip Arnold
• TEAM Solutions

2
Purpose of this session
Twofold

• Have a look at decimal fractions from a SNP
  viewpoint.

• Share a possible framework for you to use with
  the teachers in your department on other topics /
  workshops.

3
Structure of workshop

• PART ONE
• Why is this not easy? A look at misconceptions.
  
• What are the key ideas?
• PART TWO
• How can these key ideas be taught?
• PART THREE
• Who is ready to learn this?
• When should it be taught?
• Where is it going?

4
WWWWH Template

• Overview of topic from pedagogy point of view

5
Why?

• Why is this not easy?
• What are the major misconceptions / issues that
  need to be addressed?

6
Decimal Diagnostic Test

• Analyse the answers to the decimals diagnostic
  test
• What are some of the common issues /
  misconceptions that students have with decimal
  fractions?

7
Your student results

• Total for your group the number of students who
  got each question incorrect. Make a column and
  record this on your table.

• Find and list the five most common incorrect
  questions.
• What were the five most common correct questions?

8
Deeper Analysis

• Use the actual student responses to do a deeper
  analysis for questions 3d, 6a, 9 and 15.

List the particular responses that students give
and tally up how many gave that response across
your group.

• For each question pick the most common incorrect
  response.
• Discuss in your group what the misconception is
  that the students might have.

9
Question 3d

• 5.1 for

5 5 6 6
.
10
Question 3d

• 5.1 for

5 5 6 6
5.1 18/60 9 correct Yr 9
.
11
Question 6a

• Write down the bigger of the two numbers
• 0.65 and 0.7

12
Question 6a

• Write down the bigger of the two numbers
• 0.65 and 0.7

0.65 19/60 8 correct Yr 9
13
Question 9

• Add ten to 0.15

14
Question 9

• Add ten to 0.15

0.25 38/60 5 correct Yr 9
15
Question 15

• Multiply 4.17 by ten

16
Question 15

• Multiply 4.17 by ten

40.17 7/60 4.170 4/60 26 incorrect 19 no
attempt 3 correct Yr 9
17
What?

• What are the key ideas / concepts to be
  introduced?
• What do they need to know?
• What do they need to understand?
• What do they need to be able to do?
• What number knowledge do they need?

18
Brainstorm decimal fractions

• What do they need to know?
• What do they need to understand?
• What do they need to be able to do?

19
A look back to 1948

• Key idea
• Information can be told
• Concept needs to be taught
• Look at this video and explore what is
  information and what are concepts
• http//www.youtube.com/watch?v4Iv8OTmBBaM

20
How?

• How will this be taught?
• Materials
• Imaging
• Generalising
• Resources

21
Materials

• Why not money?
• Unifix cubes

22
Question One

• Use the unifix materials to solve this problem
• 6 ? 5
• 6 bars of chocolate shared amongst 5 people
• write your answer as
• ? wholes and ? tenths

23
Further examples to explore

• 6 ? 4
• 9 ? 2

24
Imaging

• Solve the following problem by imaging - clearly
  explain how you could have used the materials
• 4.2 ? 3
• Decode / Recode

25
Other problems

• 1.9 2.4
• 6.1 2.7
• 3 ? 1.8

26
Generalising

• Canon of Place Value
• 10 for 1, 1 for 10
• Use of words to link meaning and symbols

27
Who?

• Who is ready to learn this?
• What diagnostic question could I ask to assess
  what they already know / understand?

28
Place Value knowledge

• Look at numeracy framework what stage are
  decimal fractions introduced?
• What about 2 decimal places?

29
When?

• When will this be introduced?
• What prior knowledge is needed?

30
Progression

• In what order does this work suggest the
  following should be taught in?
• Decimals
• Fractions
• Percentages

31
Where?

• Where is this going?
• What comes next?

32
What about 2 decimal places?

• 5 ? 4
• Record as
• ? whole ? tenths ? _______
• What are these called and why?
• Use of decimats

33
Where else do decimal fractions appear?

• Discuss where in your current Junior programmes
  decimal fractions appear
• Rounding Book 8
• Measurement
• Estimating number, statistics
• Probability

34
Further explorations

• Purple Books
• Book 4 p4, 5, 8-9, 13, 19, 21, 28-30
• Book 5 p46-50
• Book 6 p60-62
• Book 7 p22-29, 36-37
• Book 8 p19-22, 24-25, 31, 37-38

35
Further explorations
Planning sheets www.nzmaths.co.nz AA -gt AM
36
Further explorations
Planning sheets www.nzmaths.co.nz AM -gt AP
37
Further explorations

• Link to Kath Hart tests / Kay Irwin research