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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. W hat did you see? Can you make it with these chips?
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Dynamic Dots Moving from the known to the unknown
Combine and Partition 2 to 5 without counting
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?
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.
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 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.
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)
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 • Pick a frame and screen it (do not flash it). • 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) • The write their responses on the white board and cross out the ones that do not fit.
Were you right? What’s your favorite way to make eight?