Exploring Decimal Fractions Louise Addison Pip Arnold TEAM 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. 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. 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 56.
Question 3d 5.1 for /~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 /~60 8 correct Yr 9
Question 9 Add ten to 0.15
Question 9 Add ten to /~60 5 correct Yr 9
Question 15 Multiply 4.17 by ten
Question 15 Multiply 4.17 by ten /~ /~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… TmBBaM
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 5 6 bars of chocolate shared amongst 5 people write your answer as: wholes and tenths
Further examples to explore… 6 4 9 2
Imaging Solve the following problem by imaging - clearly explain how you could have used the materials… 4.2 3 Decode / Recode
Other problems 6.1 – 2.7 3 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, Book 5 p46-50 Book 6 p60-62 Book 7 p22-29, Book 8 p19-22, 24-25, 31, 37-38
Further explorations Planning sheets AA -> AM
Further explorations Planning sheets AM -> AP
Further explorations Link to Kath Hart tests / Kay Irwin research: Link to Kath Hart tests / Kay Irwin research: