Exploring Decimal Fractions

Louise AddisonPip ArnoldTEAM Solutions

Purpose of this session

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.

Twofold:

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?

WWWWH Template

Overview of topic from pedagogy point of view…

Why?

Why is this not easy? What are the major

misconceptions / issues that need to be addressed?

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?

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.

Correct answer No.incorrect

Totalforgroup

1 Zero pointthree nine

2a Tenths

2b Tenths

2c Thousandths

3a 6.8

3b 3.74

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

Deeper Analysis

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

ANALYSIS OF MISTAKES

10 Freq0.02 110.002 52 5

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.

Question 3d

5.1 for

5 6

.

Question 3d

5.1 for

5 6

.5.1 18/~60

9 correct Yr 9

Question 6a

Write down the bigger of the two numbers

0.65 and 0.7

Question 6a

Write down the bigger of the two numbers

0.65 and 0.7

0.65 19/~60

8 correct Yr 9

Question 9

Add ten to 0.15

Question 9

Add ten to 0.15

0.25 38/~60

5 correct Yr 9

Question 15

Multiply 4.17 by ten

Question 15

Multiply 4.17 by ten

40.17 7/~60

4.170 4/~60

26 incorrect

19 no attempt

3 correct Yr 9

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?

Brainstorm – decimal fractions

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

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?v=4Iv8OTmBBaM

How?

How will this be taught? Materials Imaging Generalising Resources

Materials

Why not money? Unifix cubes

Question One:

Use the unifix materials to solve this problem…

6 56 bars of chocolate shared amongst 5 peoplewrite your answer as:

wholes and tenths

Further examples to explore…

6 49 2

Imaging

Solve the following problem by imaging - clearly explain how you could have used the materials…

4.2 3 Decode / Recode

Other problems

1.9 + 2.46.1 – 2.73 1.8

Generalising

Canon of Place Value 10 for 1, 1 for 10

Use of words to link meaning and symbols

Who?

Who is ready to learn this? What diagnostic question

could I ask to assess what they already know / understand?

Place Value knowledge

Look at numeracy framework – what stage are decimal fractions introduced?

What about 2 decimal places?

When?

When will this be introduced? What prior knowledge is

needed?

Progression…

In what order does this work suggest the following should be taught in?

Decimals Fractions Percentages

Where?

Where is this going? What comes next?

What about 2 decimal places?

5 4

Record as: whole + tenths + _______

What are these called and why?

Use of decimats

Where else do decimal fractions appear?

Discuss where in your current Junior programmes decimal fractions appear…

Rounding – Book 8 Measurement Estimating – number, statistics Probability

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

Further explorations

Planning sheetswww.nzmaths.co.nz

AA -> AM

Further explorations

Planning sheetswww.nzmaths.co.nz

AM -> AP

Further explorations

Link to Kath Hart tests / Kay Irwin research: