Investigations Blog
Robot Fingers and Multiplicative Structure
In a blog post over a year ago, I wrote about the importance of using story contexts to support students in developing mental images of the operations. In that post, I concluded: “Along with pictures, drawings, diagrams, equations, and physical models, story contexts are critical parts of a student’s repertoire of representations. In fact, it is often the case that three kinds of representations are in play: a numerical representation, a picture or diagram, and a story. Moving among these to...
read moreAnd Then, She Waited
Have you ever been teaching (or leading professional development) and asked a really good question only to be met with silence? We all have teacher moves in our back pocket for situations like this—maybe do a turn and talk, ask the student if they’d like to call on someone to help them, or ask a different question. I recently observed a third grade lesson when I saw a teacher face this exact situation. The lesson (Unit 5, Session 3.4) focused on strategies for solving division problems. The...
read more“That Seems Way Too Big”
On a recent visit to a small district in the Midwest, I got the chance to visit a third grade class that was working on division (3U5, Session 3.4). When I joined Nicole, she was in the middle of working on the following problem: Gil loves toy cars. He saved enough money to buy 32 toy cars. How many 4-packs of toy cars did he get? (SAB p. 333) Below the problem, Nicole had written I asked her to tell me about her thinking. She said she wanted to start with something she knew, which I agreed...
read moreA Grade 3 Q&A: Assessing the Multiplication Facts
Question: Why do the assessments of the multiplication facts in Grade 3 include a time limit?Answer: In Investigations, the overwhelming majority of students’ work with the facts is focused on making meaning of the operation of multiplication, building connections between problems and images that represent them (e.g. problems about things that come groups, arrays), and using what they know to solve what they don’t (e.g. how can knowing that 3x4=12 help with 6x4?). This work happens in...
read moreA Grade 3 Q&A: Why start with multiplication and division?
Question: Why does 3rd grade start with a multiplication/division unit and not addition/subtraction?Answer: We often hear from people who wonder why Grade 3 starts with a multiplication and division unit—just like it did in the 1st edition!—rather than an addition and subtraction unit. As we decided on the sequence of the units in any grade, we considered many different things. The most important was the development of mathematical content within and across grades.In Investigations 3,...
read morePuzzling Through Making Fraction Sets
Last year I volunteered in a third grade class. The school mainly uses Investigations 3. During a visit last spring, the class was working on the second session of the fractions unit. I was excited to find out about the students’ beginning understandings of fractions. I sat with a group of four students who were working on making fraction sets. Their task was to fold each of 5 sheets of paper into two, three, four, five, and six equal parts and then to label each piece. The students made 4...
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