Lesson 21

The purpose of this warm-up is to elicit student ideas about composing the same shape in different ways. While students may notice and wonder many things about these shapes, how the same shape is composed in different ways and the ways to describe the shapes are the important discussion points. Students are encouraged to carefully explain the shapes they see using the geometric language they’ve learned in previous lessons (MP6). For example, “The hexagon in one bee is made up of 2 rhombuses and 2 triangles in the other bee.”

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “The shape looks like a bee. How are these two bees similar?” (They are the same shape and size. They have two trapezoids.)
• “How are they different?” (One bee has 2 hexagons, but no rhombuses or triangles. The other has 4 rhombuses and 4 triangles, but no hexagons. One has 4 pieces all together, the other has 10 pieces.)
• “We are going to keep thinking about how to make the same shape in different ways using pattern blocks in our first activity today.”

In this activity, students create their own Pattern Block Puzzles for each other. During the activity they must adhere to mathematical constraints and are encouraged to use mathematical language to compare the different ways they can complete each puzzle. Monitor for the different ways students use the mathematical language they learned throughout the unit, including ways they identify the names of shapes they compose and the way they use words like halves, thirds, or fourths to describe ways they compose shapes out of same-size pieces (MP6).

• Groups of 4
• Give each student a piece of card stock and each group pattern blocks.
• “We’re going to use hexagons, trapezoids, blue rhombuses, and triangles to make puzzles for our partners.”

• “Trace each pattern block on the blank puzzle paper (card stock). When you’re done, trade with someone in your group to complete the activity.“
• 5 minutes: independent work time
• 5 minutes: partner work time

• Invite students to share what they noticed with members of their group and/or the class.

In this activity, students solve addition problems using money based on the Pattern Block Puzzles they sketched in the last activity.

The launch of the activity is an opportunity for students to reason which of the two designs will cost more before they complete any computations.

• Groups of 2
• “At the Pattern Block Store, each pattern block shape has a different price.”
• Display the price list.
• “Which of the two puzzles that you sketched do you think will cost more to make? Puzzle 1 or 2?”
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share responses.

• “Use the price list to figure out how much your two puzzles would cost.”
• 5 minutes: independent work time
• 5 minutes: partner discussion
• As students work, look for different addition strategies. Monitor for students who:
  • add like quantities first
  • add bigger or smaller coins first
  • add some coins mentally

• Invite previously selected students to share.
• “Is it possible to redesign the puzzle to save more money?” (Yes, I can switch a blue rhombus with two triangles.)