Making Tens

• ## Making Tens: Finding Addends That Sum to Ten

Periods: 3
Author: Susan Andrews Kunze

### Instructional Plan

Students use three different ways to find addends that sum to ten. First they make different arrangements of two number blocks that add up to ten. Then students use 2-sided counters to make and record addends that sum to 10. Lastly, students play the card game Making Tens Concentration to practice identifying addends that sum to ten.

### Preparation

For the first class period, each student will need a copy of the Making Ten Frames Activity Sheet. The teacher will need one copy of the Making Tens Overhead. This representation can also be displayed on the board. Each pair of students will need two sets of 10 snapping cubes. Each set should be a different color.

For the second period, each student will need a clean copy of the Making Tens Frames Activity Sheet, 10 two-sided counters, and a small cup.

For the third period, print a copy of the Cut Out Number Template on card stock for each student, and cut the cards apart.

### The Lesson

To begin the lesson, use 10 snapping cubes of the same color (let's say red for the sake of the directions), model the number 10 by making 2 columns of 5. Ask students, "How many cubes are there"? [10.] How many red cubes are there? [10.]. "Can you tell me how you know there are 10 cubes?" [Answers will vary.] Then introduce a second color (let's say blue for the sake of the directions). Tell the class you are replacing 2 red cubes with 2 blue cubes as you make the change. Ask, "How many red cubes are there now?" [8]. "How do you know?" [Answers will vary.] Ask, "How many blue cubes? [2] How many total cubes?" [10]. "How do you know there are 10 in all?" [Answers will vary.] Show the Making Tens Overhead to the students. Mark the overhead with "R" and "B" to show the placement of the blocks you just arranged. Write 8 + 2 = 10 on the line beneath the 10 frame. Demonstrate how the overhead could be turned 90 degrees to represent the same combination of blocks. Repeat the activity with another combination of addends to 10.

Distribute the snapping cubes and the Making Ten Frames Activity Sheet. Explain to students that they will be making different arrangements of the two colors of cubes that add to 10. They can use the activity sheet as a template for arranging the cubes in 2 columns. They will write a number sentence beneath each arrangement. Refer back to the overhead if necessary.

Observe students as they begin working, and ask them how they know they have different combinations of 10. Be aware of students who might be using an incorrect total number of cubes. If a student asks for another activity sheet, have him or her check the number sentences to see if any addends were repeated. If this occurs, it is a good opportunity to point out that, for example, 7 + 3 has the same sum as 3 + 7. Note that all combinations in this activity will inherently have the same sum. Because students are using different colored cubes, expecting students to show the commutative aspect of the combinations would be a strength for this activity.

When students are finished, have them share their ten frames with the rest of the class. Some students might not have all of the same color cubes touching, or might alternate colors. Have students discuss whether these models represent the number sentences in the same way as those that show the cubes touching. Ask students how they know it is the same or why they think it is not. Discuss the different methods students are using, why they are or are not viable, etc. If no student has used 0 as an addend, ask students how they would represent your original arrangement of 10 red cubes.

In the second period, students will use ten 2-sided counters (bean counters, disks, or pennies) to randomly make, represent, and record two addends that sum to 10 in a ten frame. Each students will receive a new copy of the Making Ten Frames Activity Sheet. On the activity sheet, above each ten frame, students label each column, depending on what counter they are using. For example, if they are using bean counters, they will label one column "Red" and the other column "White". To start, each student places the 10 objects in a cup (students should only choose two different objects), then covers, shakes, and tosses them out onto the table. Then, the student will arrange the counters to represent 2 numbers that sum to 10 and then, record each added in the corresponding column on the activity sheet. With each toss, students only record addends that are not already recorded. Be sure to point out that, for example, 2 + 5 and 5 + 2 represent the same addends. Students toss until all possible addend combinations (including 10 + 0) are tossed and recorded. As students are working, the teacher should again observe and ask questions to the students to ensure comprehension.

This activity can be done more than one time by using one or more types of two-sided manipulatives. Varying the manipulatives used when repeating this activity provides students with more opportunities to develop their visual memory of addends that sum to 10 without seeming overly repetitive.

When the teacher has determined that students have mastered the concept, this activity can be played as a game for 2 to 4 players. Each player takes a turn to toss, build, and record new sums of 10 on a new Making Ten Frames activity sheet. The first player to fill his or her recording sheet with all 6 tables of different sums of 10 wins.

In the third period, students play the card game Making Tens Concentration to practice identifying addends that sum to 10. To play, groups of 2 to 4 players make a 2 × 5 array of the cut out cards, with the numbers face down. Extra cards are placed in a pile to replace those that are removed during play. The first player flips over 2 cards from the array. If the sum is not 10, the 2 cards are replaced face-down into the array and the next player takes a turn. If the sum is 10, the player keeps the 2 cards, replaces them with cards from the extra card pile, and turns over 2 more cards in the array. Players continue to play, filling the array with extra cards until 1 player possesses all addend pairs of 10. That player is the winner.

### Assessments and Extensions

Assessment Options

1. Students may be assessed by using snapping or linking cubes to make trains that represent two numbers that sum to 10.
2. Assessment can be made by using the Making Tens: Assessment Sheet
Making Tens: Assessment Sheet
3. Students can record their combinations on large graph paper cut in the shape of a ten frame, and then glue them into a Making Tens booklet, one combination per page. Students label each number sentence and may include an appropriate fact family. To make booklets, fold and staple 3 sheets of paper together or make staple-less booklets. (In order to save time, groups of 6 can be made, where each student is responsible for one of the six pairs of addend that make 10).
4. Questioning during observation of student work can be used as a formative assessment. While doing this, make a checklist to keep track of the combinations that students know and are able to model.

Extensions

1. Play another card game: Trading for Tens. To play, each pair of students will need a deck of index cards numbered 1 - 10. To start, a player deals each player 7 cards. All of the other cards remain in the pile. Each player looks at his or her hand and puts any pair that sums to 10 in his or her pair pile. Then the first player asks another player for a card that will allow him or her to make a pair with a sum of 10. If that second player has the card, it is given to the first player. If not, the second player says "Take a card," and the first player takes a card from the pile. If the first player can use it to make a sum of 10, then he or she gets another turn. If not, the next player begins play. Play continues until all possible pairs have been made. The winner is the player with the most pairs of 10.
2. Give each student a paper bag containing 10 snapping cubes of 1 color and 10 snapping cubes of another color. Each student pulls out 10 cubes, then places those 10 cubes in 1 ten frame. Ask students who need a challenge to guess the color and the number of the remaining cubes in the bag. The student then pulls out the remaining 10 cubes and places them in a second ten frame. This provides a great illustration of the commutative property of addition for students.
3. Depending on the grade level, students may work with larger numbers, e.g. combinations to 18 or 20, using a double ten frame. This can be used in conjunction with an Illuminations app called Ten Frame.
Ten Frame
4. Introduce students to probability by dumping out ten 2-sided counters 20 times. Students will record the result every time and discuss which addend pairs occurred the most.

### Questions and Reflections

Questions for Students

1. Why are 4 + 6 and 6 + 4 considered the same pair in these activities?

[Response can be shown by changing the orientation of this pair in a ten frame or an explanation of that relationship as the commutative property of addition.]

2. What pattern can you see in the organized list of addend pairs of numbers that sum to 10?

[One number in the sequence gets larger and the other becomes smaller.]

3. Can there be more than two addends that sum to 10?

[Yes.]

4. Can you give an example of four addends that sum to 10?

[Yes, one possible answer is 1 + 2 + 3 + 4.]

5. Is there a way to keep track of the ways to make 10, ensuring that you do not repeat any?

[Yes. One way is to make one addend bigger and the other smaller by 1. Keep doing this until a repetition occurs.]

Teacher Reflection

• What were some of the ways that students demonstrated that they were actively engaged in learning by making tens?
• How did your lesson provide opportunities for differentiated instruction? Were you successful in engaging all students? If not, how could you adapt the lesson to meet the needs of students of diverse abilities?
• What aspects of classroom management worked in this lesson? What didn't work? How would you change what didn't work?

### Objectives and Standards

Learning Objectives

Students will:

• Use manipulatives to sum two numbers to make ten.
• Identify and record pairs of number addends that sum to ten.
• Develop visual patterns of numbers and addends that sum to ten.