Visualizing and Investigating Big Ideas, Grade K by Jo Boaler & Jen Munson & Cathy Williams

Author:Jo Boaler & Jen Munson & Cathy Williams [Boaler, Jo & Munson, Jen & Williams, Cathy]
Language: eng
Format: epub
ISBN: 9781119358602
Publisher: Wiley
Published: 2020-08-25T00:00:00+00:00

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Are kids struggling to come to agreement, even when they are counting? You may notice that even when students have counted the dots, they may still not agree on how many dots there are or which group has more dots. Support students by giving them counters that they can place on top of the cards so that they can move the dots to count and compare. Students can then place the dots in a line for each card, matching the counters to see which line has more dots. Alternatively, students may agree on how many are in each group but not on which is more. Ask, How can we tell which one is more? Is there a tool that could help, like counters or fingers? The counting sequence can be supportive here. If students count aloud, they can hear which number they say first and which comes after. This is a concept itself, that as you say numbers aloud, they get larger, which students may be developing in this activity.

Are kids using “bigger” to mean more dots or more space? When dots are scattered, rather than organized, the same number of dots may take up more space on the card. This group can appear “bigger” because it occupies a greater area. One aspect of conservation is that students understand that moving the dots does not change the number, no matter whether they move them closer together or farther apart. Students may need to test this idea themselves. Consider offering students counters to represent the card, count, move around, and recount. Be sure to use precise language with students, so that instead of asking, Which group is bigger? you ask, Which group has more dots?

What grouping strategies are students using? Students may use some of the counting strategies they developed in dot talks to support figuring out which group has more dots. For instance, students might cluster dots into smaller groups of 1, 2, and 3 to count the total. Alternatively, students might use these clusters to compare the larger groups. For instance, students might observe that, in the Two Sets image, the group of five dots is made of a cluster of two and a cluster of three, but the group of seven has two clusters of two and a cluster of three. By comparing these smaller clusters, they may never consider how many dots are on the card. This is an inventive and very mathematical way of thinking about the task. Be sure to draw attention to these ways of using clusters of dots to count and compare.

How do students handle equal groups? It may happen that students draw two cards with the same number of dots, though represented differently. Watch closely how students handle and name what they see, and be sure to raise this with the whole group during the discussion. This is a prime opportunity to build the language of equal. In this setting, the two groups are the same, but only in quantity or value, not in appearance.

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