Here are some diagrams that we will use to represent base-ten units.

• A large square represents 1 one.
• A medium rectangle represents 1 tenth.
• A medium square represents 1 hundredth.
• A small rectangle represents 1 thousandth.
• A small square represents 1 ten-thousandth.

1 large square labeled "one." 1 medium rectangle labeled “zero point one, or tenth.” 1 medium square labeled “ 0 point 0 one, or hundredth.” 1 tiny rectangle labeled “0 point 0 0 1, or thousandth.” 1 tiny square labeled “0 point 0 0 0 1, or ten-thousandth.”

1. Here is the diagram that Priya drew to represent 0.13. Draw a different diagram that represents 0.13. Be prepared to explain why both Priya’s and your diagrams represent the same number.

   

2. Here is the diagram that Han drew to represent 0.025. Draw a different diagram that represents 0.025. Be prepared to explain why both Han’s and your diagrams represent the same number.

   

3. For each number, draw or describe two different diagrams that represent it.

   1. 0.1
   2. 0.02
   3. 0.004

4. Use diagrams of base-ten units to represent each sum. Try to use as few units as possible to represent each number.

1. Here are diagrams that represent differences. Removed pieces are marked with Xs. The larger rectangle represents 1 tenth.

   For each diagram, write a subtraction expression and find the value of the expression.

   

   

   

2. Express each subtraction in words.

3. Find each difference by drawing a diagram and by calculating with numbers. Make sure the answers from both methods match. If not, check your diagram and your numerical calculation.