SIDEWALKS OF PRAGUE

MOE BURKHART MICHELLE KATZCMC-S

October 24, 2014

In Prague, some sidewalks are made of small square blocks of stone. The blocks are in different shades to make patterns that are in various sizes.

Figure 2

Figure 1Figure 3

Without drawing it, how many of each color tile do you think you’ll need for Figure 4?

Why do you think so?

Now draw Figure 4. How does the drawing compare with your prediction? (The grid below is not necessarily the correct size for Pattern number 4.)

What if you had to create Figure 20? Figure 100? Figure ? How many of each color tile will you need no matter the size?

 

Now draw Figure 4. How does the drawing compare with your prediction? (The grid below is not necessarily the correct size for Pattern number 4.)What if you had to create Figure 20? Figure 100? Figure ? How many of each color tile will you need no matter the size?

What questions will you ask to help students

Get started?

Find their own path to Figure 4?

To apply their idea to a larger figure?

To generalize to the nth figure?

QUESTIONS TO ASK STUDENTS1. What shapes do you recognize?2. Can you explain to me what the question is asking?3. Describe how the shapes change from one figure to the next.4. What is your first step?

5. What will you do if your first step doesn’t work?6. What observations can you make about the figure?7. What relationships can you describe between the figures?8. How big will this part be in figure 20 (looking at one part of

the figure)9. What relationship do you see between the figure number

and the number of black tiles and white tiles?

GALLERY WALK Using one post-it per poster of

student work come to consensus with your group

I NOTICE: Positive, specific, content-based

I WONDER: Comment or question that promotes revision for a better end product

How would you assess your students’understanding of this problem?1. Looking at their rule and seeing if they made a connection between the black and white tiles. 2. How they label dimension and area.3. Rubric: check the elements. Discussion with students if they can reasonably defend.4. map.mathshell.com5.

3-2-1WRITE3 things you noticed

today

2 things you wonder about

1 thing that surprised you

HOW MUCH SHOULD WE SCAFFOLD?