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At this rate... we will definitely not be smarter than a 5th grader:)   Guiding students to higher thinking (without them knowing) is pretty amazing! 

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At this rate... we will definitely not be smarter than a 5th grader:)   Guiding students to higher thinking (without them knowing) is pretty amazing! 

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You can progress through a series of t/f equations built upon what students are saying to continue to develop relational thinking and an understanding of equivalence.
Addition --> multiplication --> equivalence
1/3+1/3=(1/9+1/9+1/9)+(1/9+1/9+1/9)
2 x 1/3 = 6 x 1/9
2/3=6/9

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Representing students' thinking with fractional notation

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The part about 6/9 =
1/9 + 1/9 + 1/9 +
1/9 + 1/9 + 1/9
was really good. It shows how decomposing is related to division and helped the kids see that 3 ninths equals one third.

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I love how the teachers allowed the students to direct model and then, via a class discussion, led the students to make the connection to equivalent fractions while providing equations that matched their work. I also found the question at the end about which problem would provide the most equivalent fractions to be very helpful so that I am able to pick numbers strategically when presenting problems with fractions.

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Questioning students and having them share their ideas gives them the opportunity to verbalize their thinking and make connections.

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Being intentional in your questioning allows the students to really analyze their work and their understanding.

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Being intentional in your questioning allows the students to really analyze their work and their understanding.

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Thinking about mathematical relationships the they knew to be true.

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Sharing reasoning even when teacher can see it helps students verbalize what they understand and gives others ideas in how to solve.

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Sharing reasoning even when teacher can see it helps students verbalize what they understand and gives others ideas in how to solve.

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Yes, choosing numbers that will provide the most variety of equivalency

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Yes, choosing numbers that will provide the most variety of equivalency

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Teachers were very strategic with number choices which guided the conversation to fraction equivalence. 

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Teachers were very strategic with number choices which guided the conversation to fraction equivalence. 

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You must be very intentional with your number choices in order to guide your students.

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You must be very intentional with your number choices in order to guide your students.

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intentional numbers that will produce equivalency in responses.

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Teachers were very intentional with their questions to guide students into finding the equivalency in the problems

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Teachers were very intentional with their questions to guide students into finding the equivalency in the problems

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What sticks with you from the reading? Why?

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What sticks with you from the reading? Why?

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Using what students already know and asking questions to elicit student thinking about relationships in fraction equations.