Marian Small - One, Two...Infinity

MARIAN SMALL
·         PDF about designs and fraction lessons
·         Variety of ways to access student thinking
·         Using pattern blocks to explore relationships between fractions and fractional amounts
Getting started
• Show the kids

Ask
• Ask them to talk in pairs and to decide which of the statements below they agree with and which they don’t.
• A: There are twice as many red blocks as yellow blocks.
• B: The red area is twice as much as the yellow area.
• C: 2/3 of the blocks are red.
• D: 1/3 of the area is yellow.
• ask them to say one other fraction thing that is true about the design.

Station 1:
Use pattern blocks.
1. Build a design where: there are three times as many red blocks as yellow ones and twice as many green blocks as blue ones
2. Tell what fraction of the blocks are each colour. [Answer is:1/7 yellow, 1/7 blue, 2/7 green, 3/7 red.
3. Add another copy of your design to your first copy.
4. a) Are there still three times as many red blocks as yellow ones?
b) Are there still twice as many green blocks as blue ones?
c) What fraction of the blocks are each colour now? [all answers are yes and the same fractions]

Station 2
Use pattern blocks.
1. Build a design where:
• there is three times as much red area as yellow area and
• twice as much green area as blue area
2. Tell what fraction of the area is each colour. [Answer is: 1/5 yellow, 3/5 red, 1/15 blue, 2/15 green ]
3. Add another copy of your design to your first copy.
4. a) Is there still three times as much red area as yellow area?
b) Is there still twice as much green area as blue area?
c) What fraction of the area is each colour now?
5. Do those fractions “look right” to you?

Station 3
Use pattern blocks.
1. Build a design where:
• there are three times as many red blocks as green ones AND
• twice as many red blocks as yellow ones.
2. Tell what fraction of the blocks are each colour. [Answer: yellow: 3/11, green: 2/11, red: 6/11
3. Add another copy of your design to your first copy.
4. a) Are there still three times as many red blocks as green ones?
b) Are there still twice as many red blocks as yellow ones?
c) What fraction of the blocks are each colour now?
5. Do those fractions “look right” to you? [answer might be yes since 2/11 is not many of the blocks, 3/11 is a little more and there are more yellow than blue blocks and 6/11 is about half and about half the blocks are red]

Station 4
Use pattern blocks.
1. Build a design where:
• there is three times as much red area as green area AND
• twice as much red area as yellow area
2. Tell what fraction of the area is each colour. [Answer is:6/22 yellow, 12/22 red, and 4/22 blue ]
3. Add another copy of your design to your first copy.
4. a) Is there still three times as much red area as green area?
b) Is there still twice as much red area as yellow area?
c) What fraction of the area is each colour now?
5. Do those fractions “look right” to you? [answer: yes, e.g. red is about half the area and so is 6/11 and yellow is about half, so that’s 3/11 and blue is the rest]


·         More in depth presentation regarding fractions
·         Explores some big ideas
·         Use of a variety of manipulatives
·         Focussing on intermediate math
·         Where fractions come up in different areas of the curriculum
·         Relating decimals to fractions (grade 4 on)
·         Writing multiplicative relationships fractionally (grade 6 on)
·         Writing fractions to mean division (often grade 6 on)
·         Using fractions for probability (grade 6 on)
·         Using proportions (grade 8 on)
·         Using trig function ratios (grade 10 on)
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