M 1.7

Compose and decompose numbers up to 100: Group items into given amounts with and without remainders; Use number line or chart to sequence numbers; Count forward and backward by 1’s, 10’s, 2’s and 5’s using natural multiples

Noun - Numbers

Verb - Compose and Decompose

Related Article:

• The article below is a link to worksheets and ideas to help teachers to compose and decompose numbers
• https://www.pinterest.com/kdgworks/composing-decomposing-numbers-kindergarten/?lp=true

Instructional Strategies & Learning Tasks

Manipulative:

1. Ten Frames
2. Hundreds Chart
3. Multi-link cubes
4. Counters

Instructional Strategies

• Model anchors or benchmarks of 2, 5 and 10.
• Demonstrate ‘part-part-whole’ relationships to conceptualize numbers as being made up of two or more parts. This is the key to understanding number groupings and strengths number sense in students (e.g., 7 is a set of 3 and a set of 4 or a set of 2 and a set of 5).
• Use ten frames, hundreds chart and counters to have students count from 1 – 100.
• Use students to physically make groups of 10’s and 5’s.
• Use choral recitation for counting by 5’s and 10’s. Use number line or hundreds chart to indicate ‘hops’ or ‘skips’ between each number.
• Use counters to represent 2’s, 5’s and 10’s and count up to 100.
• Group large amounts of multi-link cubes or counters (up to 100) in 5’s and 10’s with without remainders.

Learning Tasks:

Task 1

• 3-D Numbers: Use multi-link cubes or other concrete materials to build groupings of specific numbers. How many different combinations for a particular number can students make using two parts? Allow for more than two parts if appropriate. Display and discuss each different combination. Additional possibilities: two-color counters or lima beans spray painted on one side, color rows of squares on grid paper, dot strips (strips of cardboard with stick-on dots – make lots of strips with from one to ten dots).

Task 2

• Fill the Chutes: Create a simple game board with ten “chutes” or columns of squares. Write the numbers 10, 20, 30 … 100 below the chutes. Students take turns rolling a number cube and collecting the indicated number of counters. They place the counters in one of the chutes. The object is to fill all the chutes with counters without going over. All chutes must be filled exactly: e.g., a roll of 5 cannot be used to fill a chute with 4 spaces.

Task 3

• Fill ‘Er Up: Show students the empty ten frames. Explain to students that they will be filling up the ten frames with counters. The object is to ‘fill up the ten frame’ to make groups of 10’s. Ask students to fill in the ten frames to give a total of 50. Explain that each rectangular space should have one counter only. Elicit how many counters were used and how many remainders were left. Repeat using less and more counters. Have students count completed ten frames by 2’s, 5’s and 10’s. Ask students to fill in the ten frames to make a total of 10, 20, 30, 40, 50, 60, and so on until students reach 100.

Task 4

• Forward and Backward: Ask students to represent their classmates using counters or multi-link cubes. Make groups of twos, then fives and finally tens. Ask students to count forward and backward by 2’s, 5’s and 10’s. Ask students how many remainders there were.

Task 5

• Hundred Chart Count: Students use a hundreds chart to counting to 100 by ones, twos, fives and tens. Students touch each number on the chart as they count or move a counter from one number to the next. Roll two dice. If you roll a ‘one’ on any one die, count by ones from any number your partner chooses up to 100. If you roll ‘two’, count by twos from any number your partner chooses up to 100. If you roll a ‘five’, count by fives from any number your partner chooses up to 100. If you roll a ‘ten’, count by tens from any number your partner chooses up to 100.

Task 6

• Hundred Chart Hunt: Use a large hundred chart. Cover four or five of the numbers. Vary the hidden numbers: in a row, in a column or using an ‘L’ to cover numbers in a row and column. Have students figure out which numbers are missing and discuss how they know. Ask students to write in missing numbers as they count by 2’s, 5’s and/or 10’s. Repeat until students feel comfortable filling in numbers up to 100.

Assessment Tasks

Task 1:

Give the student a bag of 100 cubes.

• Ask the student to take cubes from the bag and share the cubes equally by placing them in a variety of groups: two groups, five groups, ten groups, twenty groups, fifty groups.

• Ask the student – How did you share them? How many are in each group? How do you know you shared the cubes fairly?

Task 2:

Give the student a bag of cubes.

• Ask the student to count out cubes from the bag by 2’s, then by 5’s and finally by 10’s. Observe the student as he/she counts, separates and organizes the cubes.

• Ask the student to share a collection of cubes (25, 57, 83, etc.) among 3, 4, or 5 cups so each cup has the same number of cubes. Observe how the students handle any ‘remainder’ cubes.

• Is the student able to count the cubes correctly? Is the student able to share the cubes evenly?

Task 3:

Give the student ten frames and counters to count by 5’s and 10’s

• Does the student fill in the ten frame using 5 and 10 representations correctly?

• Does the student use more or less counters than needed to compose numbers up to 100?

Task 4:

Give the student a collection of counters.

• Ask students to arrange counters in groups of 5’s and 10’s. Ask students to identify and count how many counters form a group of 5’s and 10’s.

• Does the student count correctly by 5’s and 10’s?

• Is the student able to differentiate groups of 5’s from groups of 10’s.

• Does the student keep track of remainders when forming groups?

Task 5:

Give the student a hundred chart with missing numbers.

• Ask students to count from one to 100 by 1’s, 2’s, 5’s and/or 10’s.

• Does the student fill in the missing numbers in the number chart?

Task 6:

Give the student a hundreds chart with missing numbers.

• Ask students to write numbers on the chart.

• Can students see and identify numbers correctly?

• Ask students to count backwards and forward. Does the student count without missing numbers or are numbers missed?

Sample Lesson Plan