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 solve a variety of story problems and write addition and subtraction equations that match those problems. Students solve Put Together/Take Apart, Total or Addend Unknown problems and Compare, Difference Unknown problems. Students may solve in any way they want and write equations to match the story problem, putting a box around the number that represents the answer (MP2).
Action and Expression: Internalize Executive Functions.
Invite students to plan a method, including the tools they will use, for representing and solving the story problems. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Organization, Conceptual Processing
Required Materials
Materials to Gather
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to connecting cubes or two-color counters.
Activity
“You will solve problems about the picture from the warm up. The questions may include some of the questions you asked. Show your thinking using drawings, numbers, or words. Write an equation to match the story problem. If you can, write two different equations that match the problem.”
6 minutes: independent work time
4 minutes: partner discussion
Monitor for students who solved using drawings, can clearly explain how they solved, and wrote an equation.
Student Facing
There are 8 people at the table.
6 of the people are students.
How many are teachers?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Equation: ________________________________
Elena has 4 pattern blocks.
Tyler has 6 pattern blocks.
How many fewer pattern blocks does Elena have than Tyler?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Equation: ________________________________
Tyler has 6 pattern blocks.
Elena has 4 patterns blocks.
How many pattern blocks do they have altogether?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Equation: ________________________________
Priya has 7 triangles and 3 squares.
How many more triangles than squares does Priya have?
Show your thinking using drawings, numbers, or words.
Equation: ________________________________
Equation: ________________________________
Student Response
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Activity Synthesis
Display: Elena has 4 pattern blocks. Tyler has 6 pattern blocks. How many fewer patterns blocks does Elena have than Tyler?
“How did you solve this problem? What equation did you write?”
Record student methods and equations.
Repeat for the other problems with the same numbers.
“How are these problems the same? How are they different?” (They both have Elena and Tyler. They both have 4 and 6. In one we find the difference and in the other one we find the total. The answers are different.)
If needed, ask, “Is the total important to solving the first problem? Why or why not?” (No, because we are comparing the students.)


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