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The example about 6 kids sharing 8 pancakes was relatable for kids. Most students were able to see right away that each student would get at least one whole one. So that is a great starting point; they just need to divide the remaining two.

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Paper and pencil are better tools to get kids to think mathematically when it comes to solving fractions, as opposed to using already made manipulative

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Paper and pencil are better tools to get kids to think mathematically when it comes to solving fractions, as opposed to using already made manipulative

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"The procedure (for finding equivalent fractions) is usually introduced to students before multiplying and dividing a fraction by a fraction have been introduced, reinforcing the mistaken notion that a fraction is two seperate numbers rather than a single number with a single value." pg. 118

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Wow, mind blown! Good to know that math tools are not created equal and that problem solving with paper and pencil is much more impactful.

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Use paper to cut into portions and mark with a pencil rather than using manipulatives.

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Students need to understand that 1 whole is equal to the sum of its parts.

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Although the steps of this procedure may be easy to teach, its mathematical justification is sophisticated.

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What ideas are coming up for you about equivalence today?

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What ideas are coming up for you about equivalence today?

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Rethink how and when to use tools

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What "critical problem-solving decisions" (ECM page 117) are students making here?

(I may need to adjust tasks to include mathematical choices that get at relational thinking)