Fraction Blocks and Strategies

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My second and third graders started a unit on fractions last week.  Students are used to identifying typical pie fraction pieces.  Generally, I find students are introduced to fractions using this type of visual representation.  Students then count the amount of pieces and place that number as the numerator.  I find moving towards mixed-numbers has some students changing their strategy as they can’t just count the pieces, but they have to recognize that a certain amount of equal parts are one whole.  Based on their pre-assessment results, it seems as though my second grade and some of my third grade students are at this point.

Using a number line has helped.  Placing the fractions on the line has brought a better understanding of the placement of fractions in relation to a whole number.  Currently, students can identify certain benchmark fractions on a number line.  We’re working on bolstering this skill and connecting it to fraction computation in the near future.  Before that happens I want to ensure that they have a decent understanding of mixed numbers and where they fall on a number line.

On Thursday and Friday I introduced students to a fraction block activity.  Students were given a sheet with fraction parts.  Each block was split into a certain amount of equal square parts.

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Each student was given an envelope to put their pieces in once they were finished with the activity.  Students cut out each block and were asked to put them in order from least to greatest value.  Students were able to complete the task.

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We then had a conversation about quarters, halves and wholes.  I then gave each student the card below.

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Students placed the A block near the top of their desk and started comparing the different blocks.  The class completed the first question together.

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I then gave students time to work on the rest of the problems.  Students were then given time to use trial-and-error to find which blocks worked for each problem.  I went around to the different table groups and asked students questions about their strategies. Students ended up matching the squares with other shapes to determine what was a quarter, half, almost a half, and what happens when you combine shapes.  After about 10 minutes the class reviewed the sheet and found that some problems could be answered with multiple solutions.  Students put the sheets in their envelopes since we ran out of time.

The next day students completed some more challenging half-sheets involving their blocks.

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Students struggled a bit with this as they had to look at A as half instead of one whole.  This changed the value of all of the other blocks.  I allowed students to work in groups for about five minutes and then independently for another five.  This gave them an opportunity to gain another perspective and a different strategy.  Afterwards, I reviewed the possible solutions with the class.

Next week I’m taking this activity one step further and using the blocks without markings.  I’m borrowing this idea from Graham’s post on defacing manipulatives.

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Students will complete similar half-sheets, but without the evident markings. I’m looking forward to seeing how students’ strategies change and the math conversations that follow next week.   Click here to download the activity that I used.

 

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