Module 1 Lesson 4Understand the meaning of the unknown

as the size of the groups in division.

SPRINTS Today you’re going to do another set

of sprints.

There are 2 sprints – A and B

You will have 60 seconds to do as many problems as you can. I do not expect you to finish all of them, just as many as you can, trying for your personal best.

Your sprint will be placed face down on your desk – do not look at your sprint until I give you the signal.

Hold your pencil up when you are ready.

1 minute

SPRINTS Stop!

Circle the last problem you completed. I will read just the answers. If you got the answer right, call out “Yes!” If you made a mistake, circle it (no noise).

Touch your nose if you understand or raise your hand if you have any questions.

Now, at the top of the page, write the number of problems you got correct. This is your personal goal for Sprint B.

Thumbs up when you’re done.

SPRINTS Time to do Sprint B.

Once again, you will have 60 seconds to do as many problems as you can. I do not expect you to finish all of them, just as many as you can, trying for your personal best. Remember – try to meet or beat your number correct from Sprint A.

Do not flip sprint B over until you have been given the signal.

Hold your pencil up when you are ready.

1 minute

SPRINTS Stop!

Circle the last problem you completed. I will read just the answers. If you got the answer right, call out “Yes!” If you made a mistake, circle it (no noise).

Touch your nose if you understand or raise your hand if you have any questions.

Stand up if you got more correct on the second Sprint than on the first. (For example if I got 20 right on Sprint A and 26 right on Sprint B– I got 6 more right than Sprint A).

Keep standing until I say the number that tells how many more you got right on Sprint B. If you got exactly three more right on Sprint B than on Sprint A,

when I say three, you sit down.

Cross your arms if you’re ready.

Group Counting Let’s skip count by 2s forwards and backwards to 20.

Watch my hands to see if I change directions.

Let’s skip count by 3s forwards and backwards to 21. Watch my hands to see if I change directions.

Array MultiplicationSay the repeated addition equation

2 + 2 + 2 = 6

3 x ___ = ___

On your personal whiteboard complete the multiplication equation.

2 6

Array MultiplicationSay the repeated addition equation

10 + 10 + 10 + 10 = 40

4 x ___ = ___

On your personal whiteboard complete the multiplication equation.

10 40

Array Multiplication

Say the repeated addition equation

2 + 2 + 2 + 2 + 2 + 2 + 2 = 14

7 x ___ = ___

On your personal whiteboard complete the multiplication equation.

2 14

PROBLEM OF THE DAYThe student council holds a meeting in Mr. Chang’s classroom.

They arrange the chairs in 3 rows of 5. How many chairs are used in all?

Use the RDW process.

CONCEPT DEVELOPMENT

In order to be ready everyone needs:

18 counters

A personal dry erase board OR your math notebook

Pencil / Dry erase marker

THUMBS UP WHEN YOU HAVE EVERYTHING YOU NEED TO BE SUCCESSFUL IN THIS LESSON.

Concept Development Concrete to abstract: Division as fair-share, relate the answer to the unknown factor.Yesterday, Mr. Clark bought a new pack of 18 markers. He

shared them with me by dividing them into 2 equal groups. Now, I have a bunch of new markers for making our charts! Do you want to know how many he gave me?

What are we trying to find: the number of groups or the size of the group?

YES

THE SIZE OF THE GROUP

Your 18 counters represent the markers. Divide your 18counters into 2 equal groups by giving one to Mr. Clark, oneto me, one to Mr. Clark, one to me, and so on….

Do 18 jumping jacks when you’re finished.

In your head, using a complete sentence tell how many are in each group.

Put your hands on your head if you want to share your complete sentence out loud.

Yesterday, Mr. Clark bought a new pack of 18 markers. He shared them with me by dividing them into 2 equal groups. Now I have a bunch of new markers for making our charts! How many markers did Mr. Clark give me?

There are 9 markers in each group.

Let’s write a number sentence to show our work, starting from the beginning.

What is our total number of counters?

18We divided our 18 counters into how many equal groups?2 ÷ 2 = _____

If 18 is our total and 2 represents our equal groupsThen remind me, what does our unknown factor represent

Our quotient (answer) is the size of the groups

What is the size of our groups?

9

So how many markers did Mr. Clark give me?

Mr. Clark gave me 9 markers!

Quick Question

In what ways does dividing remind you of our work with multiplication?

We multiply when we want to find the total.

Here, we divided when we knew the total and wanted to find the size of the groups.

Concept Development Part 2: Pictorial to abstract: Analyze a picture to write a division sentence in which the solution tells the size of the group.

This is how Elena arranges her star stickers.

What does 12 represent in the picture?

What does 3 represent?

What does 4 represent?

Write a number sentence to represent Diana’s stickers where the answer represents the size of the group.

12 ÷ 3 = 4 12 ÷ 4 = 3

12 represents the total number of stickers

3 represents the number of groups

4 represents the size of the groups

Which one is correct?

Size

of t

he g

roup

= 4

Concept Development Part 3: Analyze equations for the meaning of the solution and represent the equation with a drawing.

8 ÷ 4 = ____

If 8 is the TOTAL and 4 is the NUMBER OF GROUPS what does the UNKNOWN represent?

Total

Number of

Groups

Unkn

own

Unknown = the SIZE of the groups!!

Draw a picture on your personal white board to go with my division equation. Use your picture to help you find the unknown factor, then write the complete equation.

Do 2 cross arm stretches when you’re done.

8 ÷ 4 = ____2

Problem Set