This worksheet is a worksheet to have the student's practice counting to tens as well as by tens to get to 100. The students are learning about various ways to group by tens, so in this worksheet, the teacher is having the students perform the task on their own. I would say this worksheet is more open ended then some of her past worksheets, but it still is somewhat closed because it tells the student to draw 10 objects in each shape. I'm curious as to if they recognize that 10 shapes with 10 items in it means 100. Two ways the student can go about this problem is by using their fingers and each time they hold up one finger, they put a design down, and when they get to 10 fingers they move onto the next circle and start again. Another way the student can go about this problem is by drawing and counting the number of objects they are drawing simultaneously.
The following is the steps this student took on this problem:
Me: What did you have to do in this worksheet?
Student: Um you make 10 of everything that you color.
Me: What else do you have to do?
Student: You need to count them and make a picture.
Me: How did you count them?
Student: I just counted.
Me: Did you need to use your fingers to count?
Student: No
Me: Did you just count in your head?
Student: Yea
Me: What happens when you fill all of the circles up?
Student: Um, I don't know
Me: If you put 10 in each of these circles do you know what that equals?
Student: 100
Me: How did you know that?
Student: Because 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 **student counted each circle as she counted by 10s**
This work reveals that the student is able to successfully count to 10 in each box. This student is also able to count by tens up to 100. Two ways to advance her thinking would be to give her a statement saying "Sally has 100 boxes. She needs to separate the boxes into 10 groups. How many boxes are in each group?" This would force the student to use knowledge from this worksheet to recognize making 10 groups and putting 10 boxes inside each group. Another way to advance her thinking would be to add "Explain your answer" to the worksheet because it would then force her to think about how 10 groups of 10 really makes 100 and why that makes sense. It would also give the teacher an insight into her thinking.
A very good analysis. What do you think are some other ways to represent the mathematical ideas explored in this task? How might you connect those different representations?
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