Unit 4, Lesson 5
How Many Groups? (Part 2)
Grade 6
5.1
Warm-up
Write a fraction or whole number as an answer for each question. If you get stuck, use the fraction strips. Be prepared to share your reasoning.
- How many s are in 2?
- How many s are in 3?
- How many s are in ?
Fraction strips depicting 2 in 8 different ways, by rows. First row, two 1s. Second row, 4 of the fraction one over two. Third row, 6 of the fraction one over three. Fourth row, 8 of the fraction one over four. Fifth row, 10 of the fraction one over five. Sixth row, 12 of the fraction one over six. Seventh row, 16 of the fraction one over eight. Eight row, 18 of the fraction one over nine.
Student Lesson Summary
Suppose one batch of cookies requires cup of flour. How many batches can be made with 4 cups of flour?
We can think of the question as being: “How many s are in 4?” and represent it using multiplication and division equations.
Let’s use pattern blocks to visualize the situation and say that a hexagon is 1 whole.
Diagram of 4 hexagons. Each hexagon is made up of 3 rhombuses using pattern blocks. 6 pairs of rhombuses are shown by pairs of arrows and labeled 1, 2, 3, 4, 5, and 6.
Since 3 rhombuses make a hexagon, 1 rhombus represents , and 2 rhombuses represent .
We can see that 6 pairs of rhombuses make 4 hexagons, so there are 6 groups of in 4.
Other kinds of diagrams can also help us reason about equal-size groups involving fractions. This example shows how we might reason about the same question asked earlier: “How many -cup are in 4 cups?”
Diagram with 4 rectangles, partitioned into thirds. In the first rectangle two parts are each labeled one third. Across all 4 rectangles, 6 pairs of one third pieces are circled.
We can see each “cup” partitioned into thirds, and that there are 6 groups of -cup in 4 cups. In both diagrams, we see that the unknown value (or the “?” in the equations) is 6. So we can now write:
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