Chocolate Arrays

Lately, I’ve been seeing arrays everywhere I go: at the grocery store, at the pharmacy, at the farmers’ market. And, of course, at Costco. The big, bad bulk retailer is bursting with interesting items arranged in perfect columns and rows.

Naturally, I made a beeline for the chocolate.

What follows is a quick-image string for exploring the associative property, the patterns that occur when multiplying, and the relationship between columns and rows. It supports the development of some key strategies for multiplying: doubling and halving to maintain equivalence, doubling a dimension to double to product, and using partial products to solve.

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Tricky Teens

Now that we’re moving into spring, I wanted to be sure my kindergarteners were beginning to gain a foundation for place value before moving onto first grade. The Common Core State Standards for Mathematics (CCSS-M) expect students to “compose and decompose numbers 11 to 19 into tens and ones.”  We know that seeing teen numbers in terms of tens and ones helps kids build number sense for place value in our base-ten system. My string encouraged this sort of grouping by utilizing ten frames. As is our ritual, I quickly show the images, one at a time, and I ask my kids:

            How many dots did you see?

            How did you see them?

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Dot Talk: Early Numeracy

This post is from Raquel Goya, a Kindergarten teacher at Hoover Elementary in Palo Alto, CA.  Raquel noted that, “Although my kids are young, I want them to see themselves as mathematicians, capable of constructing arguments and thinking flexibly by understanding that multiple approaches exist to solving a problem.” She has seen how her commitment to number strings and related routines “invites enthusiasm in my classroom” and says that her students “take pride in seeing their thinking represented on the board and grow as they grapple with each type of problem.” We look forward to more contributions from Raquel. Continue reading “Dot Talk: Early Numeracy”

Arrays on the West Side

We recently learned that the third grade team at Manhattan School for Children (Elizabeth Frankel-Rivera, Madelene Geswaldo, Alice Hsu and Marissa Denice) started a really cool Homework Page for their classes.  In addition to reading for 20-30 minutes a night and writing two entries in their ELA homework section, third graders are also expected to think about and solve a set of math problems.

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Photo number strings for multiplication

Here are two photos I snapped as I walked by a 99 cent store in LA. Beautiful arrays, no?  Image

I am thinking about how to use these kinds of images as the anchors for number strings, particularly for intervention work with older students.  Sometimes older kids need work thinking about multiplication, but in an age-appropriate way.  What kind of questions do you think of with this image?  One could most simply begin by asking what kids noticed about the image.  That would bring most of the interesting mathematics forward, I think. Beginning perhaps with how many boxes of hot chocolate do you see (nice numbers)?  And then, considering this is a 99 cent store, how much would it cost to buy all of this chocolate.  It reminds me of some work that Pamela Harris suggests in her book on Powerful Numeracy, in which she asks kids what is 99 plus any number?  A 99 cent store is a great way to think about what is 99 times any number?

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