Lesson 2: Practice Problems

Problem 1

Use the given key to answer the questions.

0.1 tenth shown as a rectangle. 0.01 hundredth shown as a square. 0.001 thousandth shown as a very small rectangle. 0.0001 ten-thousandth shown as a very small square.

  1. What number does this diagram represent?

    Two hundredth squares and five thousandth rectangles

  2. Draw a diagram that represents 0.216.

  3. Draw a diagram that represents 0.304.

Problem 2

Here are diagrams that represent 0.137 and 0.284.

A base ten diagram representing 0.137 and another one showing 0.284.

  1. Use the diagram to find the value of . Explain your reasoning.

  2. Calculate the sum vertically.

    A vertical addition problem of 0.137 plus 0.284 with the decimals lined up. There are 4 boxes to write in the answer.

  3. How was your reasoning about the same with the two methods? How was it different?

Problem 3

For the first two problems, circle the vertical calculation where digits of the same kind are lined up. Then, finish the calculation and find the sum. For the last two problems, find the sum using vertical calculation.

  1. Three vertical addition problems of 3.25 plus 1.0. The 1 is under the 2 in the first problem, under the 3 in the second, and under the 5 in the third.

  2. Three vertical addition problems of 0.5 plus 1.15. The .5 is over the one-tenth digit first, then over the five hundredth digit, and same in third but with 0's at the end of both.

Problem 4 From Unit 2 Lesson 9

Andre has been practicing his math facts. He can now complete 135 multiplication facts in 90 seconds.

  1. If Andre is answering questions at a constant rate, how many facts can he answer per second?

  2. Noah also works at a constant rate, and he can complete 75 facts in 1 minute. Who is working faster? Explain or show your reasoning.