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Teaching Mathematics Place Value Linear Model Presented by Dot Shea 2014

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Linear Model Number Track: Knowing how the numbers are related to each other (what comes after this number: how many more to five? How many to 10?) is essential for mental computation, addition and subtraction The linear model develops proportional understanding through the use of equal spacing and partitioning. This is pre-requisite to number line work.

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Number Ladder Write +2 at bottom of ladder On next rung write the starting number e.g.2 Write the remaining numbers on the ladder(4,6,8 etc) Write - 5 on top of ladder On next rung down write the starting number e.g. 30 Write the remaining number on the ladder going down (25,20,15 etc) Variation: Can also use with temperatures

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Number Lines – Number as length; Proportional thinking Use 2m length of rope; number cards and pegs. Place number at either end of the number line (rope) eg. 1 – 10 Ask a child to position a number card eg. 8 – discuss strategies the child could use to find the correct position eg. (halving the rope and then halving it again, etc.) Position other numbers, discussing the reason for their placement. Variation: Number lines can start from any number. Use larger numbers with older children.

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Number Lines – Difference Use 2m length of rope Position two people at intervals on the rope First person: “I am 78” Second person: “I am 108” What is the difference? (in between the two people). The difference is 30. Key Message: Subtraction is finding the difference. The difference is the answer. Number Lines - Difference

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Fractions-Linear Model

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Fraction Wall

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Fraction sticks

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Money-Change from $1

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Money- Change card

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