The purpose of this activity is for students to partition rectangles to create rows and columns of equal-size squares. In the Launch, students build an array with tiles and then represent it on a rectangle with tick marks as guidance. They will partition rectangles without tick marks in the next activity.

• “How does your equation match the array?”
• “Can you write an equation with equal addends that shows the sum of each row or column?”

• Invite 1–2 students to share their rectangles and equations for their rectangle with 3 rows and 5 columns. ( or )
• Draw a rectangle and partition to show:

  

• “How is this partition different from what we did in this activity?” (The squares aren’t the same size and the last column has 4 not 3.)

The purpose of this activity is for students to partition rectangles into rows and columns of equal-size squares. They use tiles to help them see how to draw lines to partition the rectangles. Although it is important for students to use what they know about the structure of arrays and composing rectangles from squares to partition the rectangles (MP7), it is not necessary for students’ drawings to be perfect. It is more important that students clearly intended for the squares to be equal in size and they can articulate their reasoning. If their squares are significantly different or result in more squares in one column or row than another, offer a ruler and consider having students trace tiles for practice or guidance.

• Invite previously identified students to share how they partitioned their rectangles.
• “What strategies did you use for making your squares all the same size?” (I knew I wanted _____ squares, so I did _____ lines across and down. I started by making my rows, then made the lines for the columns, and then saw how many squares it made.)