WEEK SIX: Number and Place Value

The BIG ideas covered and related concepts, skills and strategies:

Number sense, numeration and mental computation:

(Week 6 Lecture, Part 1)

Mental Computation Concept: That problems can be worked out mentally with effective organising of thinking

Mental Computation Skill: To mentally compute problems to get an answer

Strategies: Big 7 thinking strategies

Place Value:

(Week 6 lecture, Part 1)

Skill - Using the base 10 system, expanding a number using a numeral expander, reading and writing numbers, building a number that is spoken or written, writing a number that has been built using MABs

Strategies - Divide and/or multiply by ten, use the ones unit house as a 'line of symmetry'

- The value of the number depends on where you put it - A 2 in the hundred's house (200) is bigger than a 2 in the one's house (2)

- Introduce once children are using two digit numbers

- Number patterning - To the left of the decimal exponents increase positively and to the right they increase negatively

Numbers in other bases:

Other Bases:

Hours in the day - Base 24 / Minutes - Base 60 / Months - Base 12

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Reflection: Through this week's lectures, the point Romina made of children engaging in mental computation daily made a lot of sense for mathematical development. By engaging children in daily mental maths, the children are given opportunities to explore number theory as they create and initiate their own strategies, enabling higher order thinking and problem solving skills. As Romina believes and which I agree with, if a student can explain their mental strategies and use them effectively and efficiently, they should be able to use them irrespective of whether it is considered a 'prescribed' strategy.

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The Language Model:

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Teaching Strategies:

Activity: Exploring and comparing varying culture's counting and place value systems - Books discussed in Lecture Week 6.

(Week 6 Lecture, Part 2)

- Explore differing culture's place value as a class, ask high level questions extending them into higher learning, using Blooms Taxonomy - Have the class question, compare, relate, explore and critically evaluate the differing systems.

- Do they have a place holder? What patterns are in their numbering systems? Which do you think is easier? How is this different to ours?

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Misconceptions and strategies to remediate:

Misconception:

"A failure to recognise the structural basis for recording 2 digit numbers (eg, sees and reads 64 as “sixty-four”, but thinks of this as 60 and 4 without recognising the significance of the 6 as a count of tens, even though they may be able to say how many tens in the tens place)"

(http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/assessment/Pages/lvl2place.aspx)

Strategies to avoid or remediate misconception:

Have the children expand simple two digit numbers to explore the importance place value plays in showing a numeral's value. Intentionally have numbers ending in zero, to create an opportunity to talk about 0's job as a place holder.

(Blog Lovin. (2014). Place value tree [Digital image]. Retrieved from https://www.bloglovin .com/blogs/classroom-freebies-3915778/place-value-tree-3290285737)

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Australian Curriculum and Scootle links:

ACARA Links to Year 1:

(http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1)

Scootle Resource:

Hundreds, tens and units:

(https://content.echalk.co.uk/esa/Maths/units/units.html)

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Additional Resources:

Learning Resources:

These resources help children develop the concept that place value determines the numbers worth.

1. Dingoden Family Outback Yapper (n.d.). Place value card [Photograph]. Retrieved from http://dingoden.com/2009/05/ montessori-math-place-value-stamp-card.html

2. Teacher Pay teachers (n.d.). NBT printable. Retrieved from https://www.teacherspayteachers.com/Product/2nd-Grade-NBT-2043932

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Chapter 8: Extending number sense: Place Value

Nature of place Value:

- Explicit grouping or trading rules are defined and consistently followed

- The position of a digit determines the number being represented

Modelling – Ungrouped and group:

- Two ways to represent child develop place value – Ungrouped and then once there is enough to group into tens they are considered pre-grouped materials.

Proportional and non-proportional:Modelling:

- Proportional (base-ten blocks, bean sticks, popsticks – Bundled in group etc) – as the 100 bundle, is 10 times bigger than the 10 pile

- Non-proportional – (abacus, Money, counters) – Size relationship is not maintained.

Grouping and trading:

- Use loose materials to practice grouping

- Trading – Trade 1 ten block for 10 loose blocks

Chapter 10: Solving mathematical problems with mental and written strategies and estimation

Chapter 14: Extending students with number theory

- Number theory is mainly concerned with integers

Odds and Evens:

- Evens - Divisible by 2

- Odds - Not divisible by 2

- Use square tiles in activities to help children - Even numbers will create rectangles

Factors and Multiples:

- Factors - A factor of a number divides that number with no remainders

- A multiple of a number is the product of that number and any other whole number

Primes and composites:

- Prime number - A whole number greater than 1 that has exactly 2 factors; 1 and itself. For example, 13 is a price number and 1 and 13 are its factors. 10 is a composite since it has factors of 1,2,5,10

(Reys, Lindquist, Lambdin, Smith, Rogers, Falle, Frid & Bennett, 2012)