![]() ![]() In the diagram of $0.02 \times 0.03$, you can see that the area, which is the same value as this product, consists of six squares each with an area of $0.0006$. First, route each problem back to the area of rectangles. ![]() 0006$ means the same thing. To promote understanding, we suggest two approaches. This particular strategy could be thwarted by noting that $.02 \times. This strategy will break down with a problem like $0.02 \times 0.05 = 0.001$, so it's important to be on the lookout for incorrect strategies like these. For example, a student may get $0.02 \times 0.03 = 0.0006$ correct because the number of zeroes stays the same (four on the left and four on the right). Students may harbor some misconceptions or just poorly-understood procedures before beginning work on this task, especially related to the number of zeroes instead of the number of places to the left or right of the decimal point. In follow-up discussion, the teacher should make sure everyone notices how parts (c) and (d) work out, for example: It might help for the teacher to quickly demonstrate creating a grid to draw on and thinking out loud about the sample product $0.2\times0.3$. Students can quickly generate the two-by-three grid diagrams if they are provided with blank graph paper. With this task, we make sure that work is attached to a visual to set students up to understand multiplying any number of decimals. It leverages students' understanding from grade 5 about patterns in the number of zeros of a product when multiplying by powers of 10 and patterns in the placement of a decimal point when a decimal is multiplied by a power of 10 (5.NBT.A.2). Parts (a) and (b) are problems students should already be able to do as a result of their work in 5.NBT.B.7. A square is a special case of a rectangle. The area of a rectangle is given by the formula: Area b × h. The purpose of this task is for students to notice how the decimal point behaves when numbers in the same place (both in the hundreds, both in the thousandths, etc) are multiplied, and might be followed by the task 12 Rectangular Units. A rectangle is a quadrilateral with internal angles that are all right angles. ![]()
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