Exploring Numerical Relationships

Exploring Numerical Relationships

Stacks of Boxes

Opening

Stacks of Boxes

Discuss the following with your classmates.

  • For which stack of boxes can you determine the number of boxes in the stack by measuring the height of the stack?

Math Mission

Opening

Determine the number of objects in a group by using numerical relationships instead of counting.

Stacks of Books

Work Time

Stacks of Books

  • For which stack(s) of books could you determine the number of books in the stack by measuring the height of the stack?
  • For the stack(s) of books you identified, what other information do you need to know to determine the number of books in the stack?

Hint:

  • What would have to be true about the books in the stack for you to be able to tell how many books are in the stack?
  • Think about what you would divide the height of the books by to find the number of books in the stack.

Marbles

Work Time

Marbles

  • For which collection(s) of marbles could you determine the number of marbles in the collection by measuring the weight of the collection?
  • For the collection(s) of marbles you identified, the total weight of the marble collection is given. What other information would you need to determine the number of marbles in the collection if you couldn't count the marbles?

Challenge Problem

  • For which group(s) of rectangles is the ratio of the length to the width constant?
  • Given the ratio, what is the least amount of information you would need to know to find the area of one of the rectangles? Explain.

Hint:

What would you need to know about one marble to determine how many marbles there are?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about your classmates’ strategies for identifying stacks of books and collections of marbles that represent numerical relationships.

Hint:

As your classmates present, ask questions such as:

  • Why did you choose that stack or collection?
  • What are the quantities in the situation? Can you represent the relationships between those quantities using equations?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

A place where I’ve seen numerical relationships in my life is …