Understanding the Numeracy Framework Presented by Sheree Drummond sheree@gisborne.net.nzc

What is the difference between strategy and knowledge? Creates new knowledge through use Strategy Knowledge Provides the foundation for strategies Strategy is about how children solve number problems, in particular the mental processes they use. Knowledge considers the key items of knowledge that children need to acquire. What is the difference between strategy and knowledge? Give some examples

Knowledge and Strategy Examples Knowledge – What they need Number Identification, Number sequence and order, Grouping and place value, basic facts, written recording Strategy – What they do in Addition and Subtraction, Multiplication and Division, Fraction and Proportions

Working only with numbers Numeracy Teaching Model Working only with numbers Imaging Materials Using Materials Model and support children' understanding using a researched teaching model. Using materials Imaging -Thinking about what would happen on the materials Properties -Working only on numbers Teach to achieve next learning steps.

Stages of Development Stage 0 Emergent Stage 1 1 – 1 counting Stage 2 Counting from 1 on Materials Stage 3 Counting from 1 by Imaging Stage 4 Advanced Counting Stage 5 Early Additive Stage 6 Advanced Additive/Early Multiplicative Stage 7 Advanced Multiplicative/Early Proportional Stage 8 Advanced Proportional Counting Level One Level Two to Five Part-Whole

What can’t emergent counters do? Emergent – Stage 0 (Level One - Stages 1 to 3 After one year at school ) 1,2,3,5,8...? Can you get me 7 counters from the pile please? What can’t emergent counters do?

Emergent KNOWLEDGE STRATEGY Rote count to 5 at least. This child is unable to count a set of objects KNOWLEDGE Rote count to 5 at least.

One to One Counting -Stage One 1,2,3,4,5,6,7,8. Can you get me 7 counters from the pile please? What can this child do?

One To One Counting KNOWLEDGE STRATEGY Rote count to 10 at least Count a set of objects to 10 by one to one matching KNOWLEDGE Rote count to 10 at least

Counting or Adding? One of the key progressions is when the students move from counting to adding. Counters usually do not have basic number facts and /or do not know how to use them. Counters usually have an incomplete understanding of place value.

Count From One on Materials – Stage Two There are 4 counters and another 3 counters. How many are there altogether? 1,2,3,4,5,6,7. The child solves the problem by using their fingers or other materials . What else do they do?

Counting from one on Materials STRATEGY Solve simple addition and subtraction problems to 20 by counting all the objects. KNOWLEDGE Rote count to 20 at least Instant recognition of patterns to 5 including finger patterns Forward and backward number word sequence 0 – 20 Order numbers to 20 Numbers before and after in the range 1 - 20

Count From One By Imaging -Stage Three Counts in head 1,2,3,4,5,6,7,8. There are 4 counters and another 3 counters. How many are there altogether? The child counts all the objects from one by imaging visual patterns of the objects in their mind.

Counting From One By Imaging KNOWLEDGE Need … Instant recognition of patterns/add/sub facts to 10 including finger patterns Ordering numbers 0-20 Forward and backward word sequence in the range 0 –20 Doubles to 10 Say the number before and after a given number in the range 0-20 Record in pictures, diagrams, 5 and 2 is 7, 5 minus 2 equals 7 or 7-2 =7 STRATEGY Can solve addition and subtraction problems to 20 by counting all the objects and or imaging numbers in my head.

Advanced Counting – Stage Four (After two years at school) Counts on 9, 10, 11, 12, 13. There are 9 counters under there and another 4 counters under there. How many are there altogether? What if I remove 4 counters? The child counts on from the largest number. Is it OK to use their fingers at this stage?

Advanced Counting KNOWLEDGE Need … Recognising numbers 0 –100 Ordering numbers 0-100 Forward and backward word sequence 0-100 Numbers before and after a given number from 0-100 Skip count in 2s, 5,s 10s forwards and backwards. Teen numbers 10+ Doubles to 20 BF to 20 Compatable decade numbers to 100 STRATEGY Solve addition and subtraction problems by counting on or back in my head from the largest number using supporting materials then moving to imagery. Solve addition and subtraction problems by counting on in 10’s and 1’s. Solve multiplication problems by skip counting in 2s, 5s 10s. Arizona Monica

The Reality? To become a Part-Whole thinker children need automatic recall of … Facts to Ten Doubles Facts Ten and ….10 + 6 = 16 To Become a Multiplicative thinker children need to be able to recall the times tables

If I take one off the 6 and put it on the 9 it =10. 10 + 5 = 15” Early Additive Part-Whole - Stage 5 (Level Two After 3 years and/or End of Year 4) “I know that If I take one off the 6 and put it on the 9 it =10. 10 + 5 = 15” There are 9 counters under there and another 6 counters under there. How many are there altogether? The child uses simple strategies to solve addition and subtraction problems mentally

Early Additive Part Whole STRATEGY Solve addition and subtraction problems in their head by working out the answer from basic facts they know. Solve addition and subtraction problems with 2 or 3 numbers using groupings of 10 and 100. Use addition strategies to solve multiplication strategies KNOWLEDGE Recall doubles to 20 and corresponding halves Recall the names for 10 Recall the teen numbers Skip count in 2s,5s, 10s forwards and backwards Hannah Kate Louise

I think tidy numbers would be smartest. Advanced Additive Part-Whole -Stage 6 (Level Three -End of year 5 and 6) I think tidy numbers would be smartest. 63 – 40 = 23 23 + 1 = 24 63 people are on the bus and 39 people get off the bus. How many people are left on the bus? The child can select from a wide range of strategies to solve various addition and subtraction problems mentally. How many strategies do they need to be functioning at stage 6?

Advanced Additive Part Whole STRATEGY Choose from: Compensation Place Value Compatible numbers Reversibility Equal Additions for subtraction Decomposition to solve + and - problems. Use pencil and paper or caluclator to work out answers where the numbers are large or untidy Carry out column + and – with whole numbers of up to 4 digits (algorithms) Solve multiplication and division problems using known strategies eg doubling, rounding. KNOWLEDGE Identify numbers 0-1000 Forward and backward sequence by 1,10,100 to 1000 Order numbers from 0-1000 Recall + and - facts to 20 Recall multiplication facts for 2, 5, and 10 times tables.

Advanced Multiplicative - Stage Seven (Level Four- After Year 7 and 8) Tidy Numbers would be a smart strategy. 30 x 6 = 180 180 – (2 x 6) = 168 There are 28 fruit trees in each aisle of the orchard. There are 6 aisles. How many trees are there altogether? The child can select from a wide range of strategies to solve various multiplication and division problems mentally. What other strategies could you use?

Advanced Multiplicative Part Whole STRATEGY Solve +, - , x and ÷ problems with whole numbers (and decimals) using a range of strategies. Solve problems involving fractions, decimals, proportions and ratios using multiplication and division strategies KNOWLEDGE Identify, order and say forward and backward number sequence from 0 –1000000 Recall multiplication and division facts. Order fractions, including those greater than 1.

Advanced Proportional – Stage Eight (Start Level 5 - Year nine) You can make 9 mittens from 15 balls of wool. How many mittens can you make from 10 balls of wool? I can see that 9:15 are both multiples of 3. I can simplify by ÷3 and get a ratio of 3:5 ?:10 = 6 The child can select from a wide range of strategies to solve challenging problems involving, decimals, fraction percentages and ratios. The brainbox of the framework!

Advanced Proportional Part Whole STRATEGY Choose appropriately from a broad range of strategies to +, -, x and ÷ fractions and decimals. KNOWLEDGE Know equivalent proportions for unit fractions with numbers to 100 and 1000 Know fraction, decimal, % conversion for unit fractions. Order decimals to 3 places.

What does this mean for you? Assessment of all students in your class. On going use of formative assessment methods. Students grouped according to their numeracy strategy stages. Planning and sharing learning intentions with students. Use of equipment to reinforce teaching and learning. Sharing learning intentions with students. Encouraging students to talk about their learning. Using modeling books with each group. Students record in their own book Sharing ideas and supporting colleagues

Equipment Model concepts with many physical representations Place value equipment - unifix cubes - bean cannisters - iceblock sticks Number line Empty numberline Hundreds board Money Clip art and 3D counters Fly flip cards Bead frame Bead strings Tens frames Animal strips

Assessing what children know. Assess - where each child is at through oral interviewing and questioning Group according to a Childs strategy stage using the New Zealand Number Framework A useful tool - I CAN Portfolio Sheets Encourage children to self assess (reflect) know and own their next learning steps.

Grouping Examine your Class Summary sheet and look at how you might group the students. Strategy Stage for addition and subtraction is main indicator. Transfer data to Class Grouping sheet. With a partner discuss each other’s groupings.

Classroom Management The children need to be able to work in groups. You need to be able to plan for groups. Children must be able to work independently. Spending time establishing routines, systems and expectations is crucial.

Classroom Implementation Long term planning Weekly plan Model for daily lesson Learning outcomes/intentions Modelling book Taskboard

3-Way Rotation TPA Teacher Practice Practice Activity Activity Teacher

Writes and Wrongs, Student Recording How do you want your children to record their working? Why? Records the process Avoids mental overload Encourages Imaging Clarifies (and may extend) thinking How? Quality not quantity Separate pages for thinking and formal working Equipment sketched Modelled by teacher

Why is written recording important? We all need to learn and practise symbol and diagram literacy. They help to and to “park” information while you work on sub-tasks. Symbols and diagrams can ease the load on your working memory. Draw a diagram to help you solve this problem. Think about how the diagram helps you. Katy and Liam went shopping. At the start Liam had only three-quarters as much money as Katy. Liam spent $14 and Katy spent half her money. Then they both had the same amount of money. How much money did each person have left?

Learning Intentions Teaching Model Modelling Book Resource Documents Materials Planning Learner Needs Assessment Information Task Board

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