Seeing Patterns in the Count

7/28/2019 Seeing Patterns in the Count

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When young children first learn to count, they tend to view the sequenceof number names as a completely arbitrary list, to be learned by rote.The list is indeed arbitrary up to 10 but then it repeats in definite pattern:

first the ones digit goes from 0 to 9; then the tens digit increases by one and

the ones digit drops back to 0; then the ones digit again goes from 0 to 9,

and so on. This pattern continues throughout the tens and hundreds and

can then be extended to additional places as well. It is a very subtle pattern,

and even older students may not recognize it.

The goal of this section is to highlight the patterns in the number code.

Although we suggest that students work in pairs or small groups with the

Place mat, you may want to demonstrate first with the Counter or have

some students work with the Counter.

Counting to 1000

Distribute copies of Activity Sheet 2, thePattern of the Count sheet. Have the studentsput single blocks on the Place mat, one at a

time. After placing each block, students setthe Digit Flip Cards, say the number, andwrite it on their sheets. Since this is a tedioustask, you may want to assign each group ofstudents to start at a different hundred andcontinue until the next hundred is reached.Then all the sheets can be stapled together toform a type of number line.

After students have recorded the numbers to

1000, ask them to describe the patterns theysee. Students will develop their own termsto describe these phenomena. Some talkabout the up and down number patterns.

Others refer to starting over and over again. Providing time for students toshare their ideas and develop their own descriptive terms is important.

Over time, have students show a number on the Place mat and then predictthe next number or next few numbers before adding the blocks. Encouragestudents to focus on what happens at numbers such as 99 and 199. Some students

Focus Recognizing and using patterns in the

number code

Writing one number at a time,students discover thepatterns in our counting sequence.


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1-41-4refer to what happens as a ripple effect. That is, when we add 1 block to 9singles, it forms a block-of-10. We set a zero and add this block-of-10 to the9 blocks-of-10, which forms a block-of-100, and so on, rippling through theplaces. Because this ripple effect is more dramatic with the Counter, you may

want to demonstrate, using the Counter to count from 990 to 1000.

Challenge students to generalize their thinking by asking questions such as,

What is one more than 1999? one more than 20,599? one more than 99,999?

Counting Backward

After students have established a forward counting pattern, they can explore abackward count. Have them place, for example, 3 blocks-of-100, 9 blocks-of-

10, and 9 single blocks onto their mats. (Initially, for simplicity, they should notstart this activity with a multiple of 10.) Students remove one block at a time,set the Digit Flip Cards, and say the number. When they get to 390, they maywant to remove an entire block-of-10. Remind them that they must removeonly one single block at a time, and let them discover what they need to do.

As students work, ask them to describe this process. Students might also recordthe backward count on copies of Activity Sheet 2, Pattern of the Count.

When they are ready, ask them to predict the backward count for the next

number or next few numbers. Show a number on the Place mat and havethe students count back from that number without removing the blocks.Give particular attention to examples that require a change in the tens andhundreds places as well as the ones. Students can check their predictions byremoving one block at a time.

Challenge students to generalize their thinking by asking questions such as,

What is one less than 2000? one less than 35,000? one less than 10,000? one less than

100,000?

Counting by Tens and Hundreds

Following the exploration of patterns with ones, have students add andremove blocks-of-10 one at a time while they count forward and backwardby tens. Start by having students show 73 and ask,

What is 10 more?

Some students may find counting by tens difficult when they begin with a num-ber that doesnt end in zero. Some may count on by ones. Encourage students to


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1-41-4Assessing Learning

For these assessment tasks, have blocks of all sizes, a Place mat, and Digit FlipCards available.

1. Show the numeral 379 and ask the student to tell the number that is onemore. Then have the student use the blocks to check the answer. Does thestudent identify and name the number correctly without using the blocks? use materials correctly to check?

2. Show the numeral 250 and ask the student to tell the number that is oneless. Then have the student use the blocks to check the answer. Does thestudent identify and name the number correctly without using the blocks?

use materials correctly to check?

3. Show the numeral 593 and ask the student to tell the number that is 10more. Then have the student use the blocks to check the answer. Does thestudent identify and name the number correctly without using the blocks? use materials correctly to check?

4. Show the numeral 204 and ask the student to tell the number that is 10 less.Then have the student use the blocks to check the answer. Does the student

identify and name the number correctly without using the blocks? use materials correctly to check?

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Seeing Patterns in the Count