standard_description: Know and apply the Binomial Theorem for the expansion of (x + y)^(n )in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)
problem_activity: Narrative
The purpose of this activity is for students to learn stage 1 of the Match Mine center. Students use positional words to describe the location of pattern blocks within a larger shape. Students may initially describe the shapes generally or use positional words other than those introduced in the previous activity. Students need repeated experiences hearing positional words in order to develop precision with their language (MP6).
MLR8 Discussion Supports.
For each description that is shared, invite students to turn to a partner and restate what they heard using precise mathematical language, specifically positional words.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Pattern blocks
Launch
Groups of 2
Give students access to pattern blocks.
“We are going to learn a new center called Match Mine. Let’s practice describing a shape together.”
Build a shape with 5 pattern blocks.
“How could we describe where the square is in this shape?” (The square is below the hexagon.)
“How could we describe where the triangle is?” (The triangle is next to the square.)
“One partner will build a shape using 5 pattern blocks. Then they will tell their partner about the shape and their partner tries to make the same shape.”
“Remember to use positional words that will help your partner put each pattern block in the right place.”
“Keep your shapes hidden while you build them. When your partner is done making the shape, check to see if they match.”
“Take turns building and describing shapes with your partner.”
Activity
8 minutes: partner work time
Monitor for students who describe the location of each pattern block using positional words.
Activity Synthesis
Display a shape made up of 5 pattern blocks, including a triangle.
“How would you tell your partner where to put the triangle?”


aligns: no