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Times tables

Explore the role of timetables in Mathematics

Year 1 -10

Julia Crawford

jcrawford@cognitioneducation.com

cognitioneducation.com

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Tensions

Long running debate about times tables

Importance … by when? Just use a calculator?
How to best teach times tables?
Understanding and/or memorising?
Speed important?
Transitions between sectors primary/intermediate/secondary

In this workshop we will explore these questions and share some resources to support the learning of multiplicative thinking (and times tables) across all year levels.

^{©Cognition Education 2018}

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Current context

Curriculum refresh: clarity (understand, know, do), progress, phases of learning
Literacy and Mathematics strategy
NCEA Numeracy (and Literacy) Co- requisites
NCEA Review of the Achievement Standards
Royal Society Report
Media and community interest

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Jo Boaler visit to New Zealand

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Times tables as part of multiplicative thinking

^{©Cognition Education 2018}

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LPF Multiplicative thinking

This progression focuses on students' ability to think multiplicatively as they solve multiplication, division, and proportional problems involving an extended range of whole numbers, decimals, fractions, ratios, and percentages, and in a range of contexts.

3. The students solve single-digit multiplication and division problems by using additive thinking strategies, including skip counting, repeated addition, and repeated subtraction.

4. The students solve single-digit, single-step multiplication problems by applying known multiplication facts or by using known facts to derive unknown ones. The students solve simple division problems by using known multiplication facts or by trial and error with different-sized groups.

5. The students use their known multiplication basic facts and place-value knowledge to solve multiplication and division problems involving single-digit multipliers or divisors.

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^{©Cognition Education 2018}

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LPF Multiplicative thinking

This progression focuses on students' ability to think multiplicatively as they solve multiplication, division, and proportional problems involving an extended range of whole numbers, decimals, fractions, ratios, and percentages, and in a range of contexts.

8. The students demonstrate flexibility and a strong number sense as they estimate and solve complex problems that involve whole numbers, decimals, fractions, and integers.

9. The students apply proportional thinking to solve real problems involving percentages, rates, and ratios, and form one- and two-step algebraic equations to solve for an unknown

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^{©Cognition Education 2018}

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Teaching times tables and multiplicative thinking

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Early ideas

Equal groups
Repeated addition
Skip counting

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Multiple representations

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Shared by Jo Boaler, Waikato 2019

^{©Cognition Education 2018}

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Arrays to Areas

Phases of experiences:

Materials
Pictures of dots in arrays
Pictures of squares (to replace dots)
Regions (area model)

Whole number
Decimals

Generalise: algebra

^{©Cognition Education 2018}

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Areas to algebra

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Numeracy Project was not about teaching a sequence of increasingly sophisticated strategies…
The framework is a developmental structure to support teachers understand what they see as students learn to calculate

Strategies

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The goal

To be able to use strategies efficiently and flexibly…

… Not to know lots of strategies!

^{©Cognition Education 2018}

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Knowledge

In The Number Framework a distinction was made between strategy and knowledge.
It is important that students make progress in both sections of the framework.

The application of number knowledge and mental strategies is often described at ‘number sense’. Strongly developed number sense leads to algebraic thinking.

^{©Cognition Education 2018}

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Suggested order

x2 (addition doubles) then commutative property,

x10, x5, x1, x0 then square facts

Then x3, x4, x9 …

Which leaves x6, x7, x8

Students can keep track of their ‘mastered’ facts on a similar grid.

^{©Cognition Education 2018}

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Multiplication grid continued…

5^th Grade Mind Set Mathematics (Jo Boaler)

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What do you notice? What do you wonder?

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Steve Wyborney

Multiplication course on YouTube

12 Chapters …with a YouTube playlist in each Chapter.
Easy to share videos or chapters with students

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Not your mom’s flashcards

Conceptual understanding of multiplication

Gflectchy: Subitizing flashcards

You Cubed:

Matching, multiple representations, no time pressure

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Multiplication array/grid game

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Rote learning ? Speed?

Teaching comes before practice

There’s 5 steps to mastering the multiplication facts:

Step 1: Break up the facts into manageable chunks.
Step 2: Make the facts concrete with a simple visual.
Step 3: Teach your child to use easier facts as stepping stones to the harder facts.
Step 4: Practice each times table on its own until it’s mastered.
Step 5: Practice a mix of multiplication facts.

It depends !

No matter how old your child, try to keep practice time relaxed and positive. Multiplication timed tests and drills aren’t necessary unless your child thrives on time pressure and finds it satisfying to beat the clock.

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Games

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Whānau

Important to discuss/share why we learn times tables and ways to support home exploration of times tables facts.
Give out resources and games to play over the weekend or school breaks.
Introduce ways to review times tables in newsletters and at whānau evenings

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Top tips for parents

Top tips for parents:
Be positive
Point out the maths in everyday life
Praise your child for effort rather than talent
If you struggle with maths yourself, find ways to improve your level of maths