Teaching Mathematics Place Value Use of Manipulatives Presented by Dot Shea 2012

Beliefs underpinning the teaching of mathematics  All kids can do mathematics  Teachers can make a difference  Mathematics is about patterns and structure

The teaching of mathematics  Children need to learn through a variety of modes and different representations. l l l l l l l l l l l l

 Children need to be actively involved in representation. 25 divided by 5 equals 14 (non-literacy shed) The teaching of mathematics

Subitisation Seeing the different groupings builds the understanding that even though the combination changes, the VALUE of the number stays the same. Numbers 1 – 10 need to be flexible and established before going onto other concepts eg. addition and place value. Children need to be able to hold a visual representation of the number in their head, and be able to manipulate the number mentally. This will build mental computation skills.

To develop flexibility in mathematical understandings use different representations of same number ◦ Linear – number track, lines ◦ Set – collections of objects ◦ Area – ten frames, hundred frames Models of number

Area Model Ten frames, Hundred frames Numbers to 10, 100, 1000, fractions, decimals, percentages etc

Position and Order Number Grid (rubber mat on floor 10 x 10) Each student given a number/s (Try 26; 36; 47) Sort the numbers from smallest to largest Ask the child to position their numbers on the number grid (with 1 in the top left corner and 100 in bottom right) – observe if child identifies the position by recognizing the pattern or by counting on. and/or Teacher requests number/s randomly e.g numbers in the 90’s, 60’s, teens and/or add the rest of the numbers Variation: Can also start at a different number eg Can use for Fractions, decimals, percentages

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.

Number Ladder – using whiteboard pens 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

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.

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

Set Model

Place Value Hundreds Tens Ones Total Place 35 counters in the ones column Write 35 in the total column How many ones are there? Move 10 counters into the tens column How many all together? How many tens? How many ones? Answer still 35! Continue moving 10 counters each time until 3 tens and 5 ones – still 35! 35 ones = 35 1 ten and 25 ones = 35 2 tens and 15 ones = 35 3 tens and 5 ones = 35 Introduce 100’s column - Change to tiny tens and hundreds frames

Place Value Hundreds Tens Ones Total This understanding is critical for understanding renaming in subtraction tens and 16 ones The value doesn’t change- we are just renaming it.

Place Value Ties (place value cards), Fans, Houses, Magnetic Numbers, 100’s frames, Tiny 10 frames Need to provide a range of activities for flexibility. If students can use a range of representations they will understand place value

Beliefs underpinning the teaching of mathematics  All kids can do mathematics  Teachers can make a difference  Mathematics is about patterns and structure  Children need to learn through a variety of modes and different representations.  Children need to be actively involved in representation.