PreK to 2nd
Susan Andrews Kunze
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.
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
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
Making Ten Frames Activity Sheet
Making Tens Overhead
Cut Out Number Template
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?" . "How do you know?" [Answers will vary.] Ask, "How many blue cubes?  How many total cubes?"
. "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
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.
Questions for Students
1. Why are 4 + 6 and 6 + 4 considered the same pair in these
[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
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
3. Can there be more than two addends that sum to 10?
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.]
Grade: PreK to 2nd, 3rd to 5th
Play a matching game with different representations of equivalent items.
Grade: PreK to 2nd
Building Sets of Ten