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# Investigations Blog

## Does 80% of 65 = 65% of 80?

I recently read Digging Deeper: Making Number Talks Matter Even More by Ruth Parker and Cathy Humphreys. (This book is a follow up to their book Making Number Talks Matter.) Both books are brilliantly written and describe the authors’ process and thinking about what I consider the original number talks—a 10-15 minute daily routine where students solve computation problems mentally and discuss their strategies. One quote from Digging Deeper caught my eye about the power of number talks, and...

## A Grade 5 Q&A: Percents

Question: Why was the work with percents taken out of the 5th grade curriculum in the 3rd edition? Answer: In the 1st and 2nd editions of Investigations, there was a unit (Name that Portion and What’s That Portion?) that included lessons that connected what 5th graders already knew about percents to what they already knew about fractions and decimals. These concepts were taught together, rather than separately, and built strong conceptual understandings of the meaning of percents and their...

## From “Defective” Fractions to Infinite Equivalents

On a recent site visit, I was observing in a fourth grade classroom. The teacher started the lesson (Unit 6, Session 2.1) by writing “3/2″ on the board and asking students to name the fraction. Most said “three halves” although one or two said “two thirds.” The teacher then displayed two blank 4 x 6 rectangles. She established that one rectangle was the whole, and asked students to use their copy of the rectangles to draw a representation that showed 3/2. The math coach called me...

## The Lesson? Students Never Cease to Surprise Me

On a recent visit to a school in a small city in the Midwest, Karen and I joined a class of 5th graders as they learned a game in Unit 3 called Roll Around the Clock. In the previous session, students used a clock to find and name fractions and equivalent fractions. For example, if the minute or hour hand moves from the 12 to 3, it has rotated 3/12 or 1/4 or 15/60 around the clock. Students would use these ideas in this lesson. In this game, players take turns choosing which of two dice to...

## Puzzling 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...