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Lesson

3rd grade math - interpreting multiplication & division

Clip 5/9: lesson part 2a

Overview

Mia Buljan’s 3rd-grade students use manipulatives to help them with a multiplication/division equal-grouping-scenario problem following a structure similar to that of this word problem (one of the problems available to the students for today’s activity): “Sam's dad bought 24 hot dogs for Sam and his 3 friends. How many hot dogs can each of them have?”

Teacher Commentary

MIA BULJAN: There were several cards they needed to connect in this problem solving lesson. A word problem, a word form, and a number sentence are the three [kinds of cards] that I chose to focus on with this class. In this clip, I am struck by three things. The first is how reading comprehension might affect their math logic; the second is my role as what I call “a match maker”; and the third is how incredibly difficult it was for this particular group to connect the word-form cards to what they had done on their trays.

When I set up this problem solving lesson, I knew a few things about this class. I knew that they were very used to reading math stories, constructing them with tools on their trays, and explaining what they had done, because this is how most of our math block had been progressing. I also knew that the wording would be tricky for them, particularly on the division situations. I wanted them to focus on discourse — to explain their thinking to each other.

For these reasons, I chose to start with the word problems, because this is their wheelhouse and where they had the most access. I also chose to limit the cards to 7 or so situations. There are 32 students in this class, and I knew that I wanted to have more than one child working on the same problem, so that they could get into small groups and compare their strategies and come to an agreement about what the problem was asking.

The first thing I notice is that some students who are struggling with making sense of the word problem are possibly experiencing more of a reading comprehension fail, as opposed to a math-logic issue. When the videographer asks one student, for example, to read the problem he is solving, he begins to read the card and does well with the stem of the situation. But, as he approaches the question of the situation, his reading peters out, and he makes errors in reading the words. Small prepositions and pronouns aren’t necessarily going to interfere with a child’s ability to understand a narrative story, but they can make a huge difference in interpreting a problem solving situation. The student’s problem reads: “Sally bakes 15 cookies. She puts them in bags of three. How many bags of cookies did she make?” His reading falters over “bags of three” and comes out as “in three bags.”

We see how this affects his interpretation of the problem, as he actually goes with several ways of constructing the cubes. First, he uses three ten sticks to represent the bags, and gives each “bag” 5 cubes. He then creates a set of 45 cubes constructed three at a time (because, he tells us, “3 times 5 is 15”) and we watch him piece together the groups of three cubes into long trains of 15 cubes, for 3 groups of 15 and 45 total. Neither of these constructions quite captures the problem he is solving, but he has pulled out the 3, the 15, and knows there’s a relationship there, and he comes up with different iterations of what he knows about 3 and 15 together.