Dynamic Dots

Moving from the known to the unknown

Combine and Partition 2 to 5

without counting

Start with what is known

• Show it• Talk about it• Describe it• Flash it

After flashing – but still screened

• What did you see? • Can you make it with these chips?• Does yours look like mine? • Lets check. (now unscreen)

Let’s try another one

Watch carefully!

Tell me what you saw.

• Have the student describe what they saw. • Affirm what is right.• Ask questions that will lead to descriptive

language (where, how many, what color)

I saw 5!

T: Yes, there are 5. Tell me more.S: There was one red one and the rest were blue! T: You are right – there is a red chip. Where was the

red chip?S: In the middle.T: So there was one red chip in the middle, how many

were blue? S: Four!!T: Can you make it?

With collection still screened

• Give child a collection of 5 two sided chips.• Show me what you saw.• Does your five look like mine?• Now unscreen and check to make sure they

are the same. • Lets try another one.• Ready?

Tell me what you saw.

A “shift in the chips”

Moving from the familiar to the unfamiliar

Moving from regular spatial patterns to irregular spatial patterns – with structure.

Once children are comfortable talking about groups with 2 colors use 1 color

• Once children are comfortable (not facile) with combinations and partitions of one number introduce another number.

• Let them become comfortable with that number then begin to switch between these two numbers when flashing and screening.

• As children develop more familiarity move to random irregular dot patterns.

Now it’s time for random irregular dot patterns

Additional Activities to help solidify the learning

• Show me that on your fingers• Talk about and record the partitions

(remember to share the pen!)• Have students make their own random dot

patterns (one or two colors)• Use partially screened dot patterns

Partially screened irregular dot patterns

Partially screened dot patterns

Tell the student:There are 5 dots and two are out.

Ask:How many are under the screen?

After their response let them check.

Moving on to 6, 7, 8, 9 and 10

Combine and partition 6 to 10

Ask the student what they see. Have them count the dots and describe it by stating the color as well.

Watch it change

• With the collection still unscreened, change one chip. Ask the student to describe what they see now. If needed prompt them with: How many are blue? How many are red? How many is that all together?

Continue to change one chip at a time and ask that same question each time.

• What do you see?

Use structure to help organize thinking

Give the child an empty ten frame and have them organize the chips by following your directions.

Put 5 in the top row and 2 in the bottom row.

Put 3 in the top row and 4 in the bottom row.

Constructivism at work

• Let the child create their own way to organize the chips on the ten frame.

• Have them describe what they have made. (Note: they may need guidance about keeping like colors together, keeping the chips in groups and not spreading the dots out all over the ten frame)

You might get something like this

Or this

Next step

• When they are making combinations where the colors are grouped and the chips are grouped then have draw their pattern on an empty ten frame.

• Make another one and draw it on another empty ten frame.

• Let them create their own patterns

You might get patterns for 7 that look like this:

Otherwise known as 6 inside and one outside

Or this…

Otherwise known as 8 remove 1

Guidelines for letting students create ten frames

• Allow kids to think outside the box. By watching what they do you can get insight into how they are using what they know.

• If what they make is too inefficient don’t bother arguing too much about it. Just don’t bother using that particular ten frame when you work with it.

• If they don’t make a pattern you believe is important – join in the fun and make it yourself.

Flashing and Screening

• Using the ten frames that you and your student have generated: – Start by showing ten frames that only have a set

number of dots. (e.g. “These ten frames have 7 dots tell me what you see.”)

– Later can mix the numbers being represented on the frames.

20 Questions

1. Pick a frame and screen it (do not flash it).2. Ask the student, “This frame has 7 dots on it,

what do you think it looks like?”- You choose whether you will let the student guess

the whole (5 on top and 2 on the bottom) or only part (5 on top)

3. The write their responses on the white board and cross out the ones that do not fit.

8 dots on this ten frame what does it look like?

Were you right?

What’s your favorite way to make eight?