2. Module 7 Lesson 31 & 32 Explore & Create Unconventional Representations of One Half

3. Mixed Multiplication SPRINT 2 minutes End

4. Multiply & Divide 5 x 4 = _____ 20 5 x 8 = _____ 40 7 x 8 = _____ 56 6 x 4 = _____ 24 6 x 8 = _____ 48 15 ÷ 3 = _____ 15 30 ÷ 6 = _____ 5 18 ÷ 3 = _____ 6 36 ÷ 6 = _____ 6 28 ÷ 7 = _____ 4

5. Problem of the Day Maria draw a 6-inch by 8 inch rectangle. She shades one half of the rectangle. What area of the rectangle is shaded? 8 in 6 in 4 in A = 6 in x 4 in = 24 square inches. The shaded part of the rectangle has an area of 24 square inches.

6. Concept Development Study these images. Tell me which shapes shows one-half shaded, and explain your reasoning. These shapes show one-half shaded because EQUAL PARTS of the shape are shaded and unshaded.

7. Concept Development Do we know whether these shapes are partitioned exactly into halves? NO, we looked at them and made our best visual estimate, but we don’t know whether the parts are precisely ½ shaded.

8. Concept Development Let’s make some shapes of our own, and work to ensure that we have shaded EXACTLY one half. You will need the following supplies: Two squares templates One crayon, color of your choice

9. Concept Development How many unit squares are on each square template? To shade exactly half, how many square units can we color in?

10. Concept Development RULES: 1.Plan your design before you begin. 2.Shade exactly 18 squares on each template. 3.Use only one color on each template. 4.Shade each template differently. 5.Be as creative as you can! 6.Finish in 5 minutes.

11. Stretch Break!

12. Check Yourself! Hannah traces square-inch tiles to draw 3 larger squares. She draws the 3 large square side by side to make a rectangle. She shades on-half of each larger square as shown: a.Do you agree that all 3 squares are one half shaded? b.What is the area of the rectangle? c.What is the total area of the shaded space? Yes, all the rectangles have 16 unit squares, and 8 are shaded. The area of each square is 4 x 4 = 16 unit squares. 16 x 3 = 48 unit squares. 48 ÷ 2 = 24; 24 unit squares are shaded.

13. Concept Development Now we are going to represent one-half shaded a different way. This time we’ll use circles! You will need two circle templates to work with. The circles don’t have grids like the squares did. How can we work with them to accurately show one half a circle? We can use the center dot as a marker, and fold the circle in half.

14. Concept Development Take one of your circle templates and fold it in half as exactly as possible. Make sure that your fold crosses through the center dot. Fourths! Take the second circle template and fold it in half, then in half again. When you unfold it, what fractional unit did you create?

15. Concept Development Why might fourths be useful for representing one-half? If 2 fourths are shaded, it will represent one half. But, we could shade opposite fourths to make the shading more interesting!

16. Concept Development Now, fold the “fourths” circle back up, and fold it in half a third time. What unit have we made this time? Eighths!

17. Concept Development What other ways, besides folding, are there to creatively represent one-half with your circle?

18. Concept Development Creative Ways to Represent One Half Shading Erasing shading and redrawing it in another section Using a ruler to mark sections and shade them in.

19. Concept Development Now shade both of your circles to show one- half RULES Shade each circle to show ½ Use only 1 color for each circle Shade each circle differently Be as creative as you can! You have 5 minutes

20. Museum Walk Please display your squares and circles on your desk. When I say “MIX” move around the room, and when I say “STOP” use the Table on Problem Set 31 to analyze shapes created by other students. We will do this FOUR times, so you can analyze four shapes.

21. ONE-HALF QUILT SAVE one CIRCLE shape to use for your problem set. When called by the teacher, bring up one circle and both square grids and glue them onto the ONE-HALF QUILT for us to display.

22. PROBLEM SET