Reflection: Developing a Conceptual Understanding The Purpose of Zero - Section 2: Purpose of Zero


It is important for students to develop a conceptual understanding of why the zero makes a difference when we are writing numbers, especially money. Students need to understand that if they write $3.9, it could be $3.09, but it is also $3.90 so the zero plays a big part in the difference.

When we put the numbers on the board today the first student wrote $3.9 for three dollars and nine cents. I asked if everyone agreed and many did not. I then asked for another volunteer to come up and write it a different way. They wrote $3.09. I then told students we would leave those for a minute and try three dollars and ninety cents. The first student wrote $3.90 but there were still hands up so another student came up and wrote $3.090. 

With the 4 examples, we were able to really look at the differences, think about how money only and always has 2 places in the cents portion after the decimal point and to think about what those places mean. We talked about how many dimes and how many pennies $3.09 and $3.90 would have. We took out the large paper coins to display this and see the differences. 

When we went back to our numbers and I checked for understanding by asking students to write which of the first 2 represented three dollars nine cents, and which of the second two represented three dollars and ninety cents, everyone was correct. 

Later as they wrote price tags for their own creations, only one child wrote $22.9 which she told me was twenty two ninety. I helped her think about what we had said about having only and always a tens and a ones place and she quickly fixed her number. I reminded her that change is always written with a dimes and a pennies place. 

Students have demonstrated an understanding of tens and ones in the past, so connecting money to that understanding helped to build a scaffold with which to remember the importance of zero in money as well as in the writing of 3 digit numbers containing a zero. The structure of numbers is important for students to focus on. If they can not grasp the fact that the placement of zero changes the number, then it is important to do additional activities counting dollars, dimes and pennies and recording how many of each one. (I would take a group aside and give them 5 dollars, 9 dimes and 9 pennies each. I would ask them to take the amount of 3 dollars and 20 cents. How many dollars did they take (3), how many dimes? (2) how many pennies (0). I would write the number for them as they told me how many of each place. I could repeat this activity a number of times until students were comfortable adding the zero to the number and realizing its importance.)

  Which one is it
  Developing a Conceptual Understanding: Which one is it
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The Purpose of Zero

Unit 10: Money
Lesson 3 of 7

Objective: SWBAT use zero to hold a place when adding and subtracting money amounts

Big Idea: Zero makes a difference, depending on where it is. It may be worth nothing, but it has a special place in numbers.

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Math, Money, rounding, estimate (sums and differences)
  55 minutes
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