After students have mastered expressing number relationships using the tens frame verbally, they can then use the tens frame to connect the number relationships they have discovered to addition and subtraction equations. At first, students should work only within 5 in order for students to use the number 5 in a similar manner to the number 10. Rather than simply discussing the relationships found between numbers as in previous examples and activities, the teacher should guide students in constructing first addition, then subtraction problems (Flexer, 1986).
The activities from the previous post can be used to create addition and subtraction equations. For example, using activity 7 a student rolls a 4 using the die and places that many counters on the tens frame. Using the sentence frame, a student would construct the sentence “I have 4, I need 6 more to get 10.” The student could then write down the equation 4 + 6 =10. The student could also write 6 + 4 = 10 following the commutative property of addition.
For more advanced students, you could also introduce the idea of fact families. Fact families are four equations that are related by the same three numbers (get it, family?...ahaa!). For example...
4 + 6 = 10
6 + 4 = 10
10 - 4 = 6
10 - 6 = 4
As students become more familiar with certain facts, they can use the familial ties to solve related problems. If a student encounters the equation 10 - 4 = d and they are fluent in the relationships between fact families, the will realize that 4 + 6 = 10, so 10 - 4 = 6. Again, all of this relates back to familiarity (and to an extent, mastery) of the tens frame.
This tens frame shows 6. The 6 anchors to both 5 and 10. In relationship to 10, 6 is 4 less than 10(or 6 needs 4 more to get to 10). In relationship to 5, 6 is one more than 5, or 5 needs one more to get to six. A child fluent in this vocabulary will be able to "cross over" and make equations based off of these relationships with the guidance of an adult (Learn NC, 2015).
While most research I have thumbed through does not insist on practicing these skills everyday, we know that repetition in many cases means reinforcement. It is also the time for you as the teacher or parent to see which children are still struggling with number relationships in reference to 5 and 10. If students are not able to fluently state those relationships, they are not ready to start linking the relationships to addition and subtraction equations.
I have included some games and activities to scaffold this concept for your students below.
Activity 1: Five-Frame and Ten-Frame Tell About With Equations
·
Standards addressed:
o
K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5, K.NBT.A.1
o
1.NBT.B.2, 1.OA.B.3, 1.OA.B.4, 1.OA.C.5
o
2.OA.B.2
·
Materials: five-frame (a halved tens frame) or
ten-fame, 10 manipulatives.
·
Tell students that they are only allowed to put
one manipulative in each square on the five-frame or ten frame.
·
Ask the students to show the number 3 on their
five-frame. Ask students to share what they can learn about the number 3 from
their mat. Then, guide students in writing down equations that match what the
five- or ten-frame shows (i.e., 3 + 2 = 5, 5 – 2 = 3) (adapted from Van de Walle, 2003).
Activity 2: Tens Frame Flash with Equations
·
Standards addressed:
o
K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5, K.NBT.A.1
o
1.NBT.B.2, 1.OA.B.3, 1.OA.B.4, 1.OA.C.5
o
2.OA.B.2
·
Materials: playing card-sized tens frames
showing numbers 1-10.
·
Students take turn flashing the cards to their
partners. The partner states the number shown on the card as quickly as
possible. The student then states an equation that matches the number shown.
For example, if the number shown is 7, acceptable answers would include 7 + 3 =
10, 3 + 7 = 10, 10 – 7 = 3, and 10 – 3 = 7.
·
Students could also create equations in
relationship to 5. If the number 7 was shown,
correct answers would include 5 + 2 = 7, 2 + 5 = 7, 7 – 5 = 2, and 7 – 2
= 5.
·
This activity can be differentiated for
higher-level learners by adding a second ten-frame to the card and working with
numbers to 20.
·
If the student is correct, he or she keeps the
card. If the student is incorrect, the card is returned to the deck. The game
is played until the student has earned all the cards. Partners then switch
(adapted from Van de Walle, 2003).
Activity 3: Roll, Create, and Record
·
Standards addressed:
o
K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5, K.NBT.A.1
o
1.NBT.B.2, 1.OA.B.3, 1.OA.B.4, 1.OA.C.5
o
2.OA.B.2
·
Materials: tens frame, a ten-sided die, 10
manipulatives, recording page
·
Students roll the die and create the number
shown on their tens frame using the manipulatives provided.
·
Students discuss the relationship between the
number shown and ten. Students then record an equation which relates to the
number shown on the tens frame.
·
This activity can be differentiated to include
fact families. In this version, students would not only show one of the
equations that could be made with the tens frame, but the other three equations
from the fact family as well. For example, if a student rolled a 3 on the die,
the student would list the following equations: 3 + 7 = 10, 7 + 3 = 10, 10 – 7
= 3, and 10 – 3 = 7.
Activity 4: Backwards Bingo (Doubles +/- 1)
·
Standards addressed:
o
K.OA.A.1, K.OA.A.3, K.OA.A.4, K.OA.A.5, K.NBT.A.1
o
1.NBT.B.2, 1.OA.B.3, 1.OA.B.4, 1.OA.C.5, 1.OA.C.6
o
2.OA.B.2
·
Materials: one “thinking strategy” board and one
“sums” board (see Figure 4 for examples), calling cards, cover chips
·
Students begin with their boards blank. The
teacher pulls one calling card which have doubles plus or minus one facts such
as “7 + 7 and one more” or “4 + 4 and one less”. Students then cover up the
equation on the “thinking strategy” board and the answer on the “sums” board.
·
The student with four covered on one or both
boards (teacher’s discretion) in a horizontal, vertical, or diagonal pattern
wins the round.
·
The teacher should lead this games several times
in a small group until students are comfortable with the process. Students may
then play this game in a small group with one student being the “caller” while
others play the game (adapted from Myers & Thorton, 1977).
15
|
3
|
free
|
7
|
5
+ 4
|
4
+ 3
|
2
+ 1
|
free
|
|
7
|
17
|
19
|
11
|
8
+ 9
|
7
+ 8
|
6
+ 5
|
8 + 7
|
|
5
|
13
|
11
|
17
|
2
+ 3
|
5
+ 6
|
7
+ 8
|
9 + 8
|
|
9
|
free
|
13
|
15
|
free
|
6
+ 7
|
4
+ 5
|
3 + 4
|
Figure 4 shows examples of both the
“sum board” (board on the left) and the “thinking strategy” board (board on the
right).
Activity 5: Sharing the Love (Doubles + 2)
·
Standards addressed:
o
K.OA.A.3, K.OA.A.4, K.OA.A.5, K.NBT.A.1
o
1.NBT.B.2, 1.OA.B.3, 1.OA.B.4, 1.OA.C.5, 1.OA.C.6
o
2.OA.B.2
·
Materials: Balance beam, 20 unifix cubes of two
different colors (10 of each color).
·
The
teacher presents the student with a doubles-plus two equation such as 8 + 6 =
s. The student then places the correct number of cubes on each side of the
balance beam. Each addend should be a different color.
·
Ask student “how can we make each side of the
balance beam even out?” The student should reply “by moving one cube over”.
·
Show the student that the original equation can
be change into the doubles fact 7 + 7 = 14.
·
Students could also express the changes made to
the balance beam (i.e., 8 – 1 = 6 + 1).
·
Have students record both equations on a
recording page or in their math journal (adapted from Myers & Thorton,
1977).
Activity 6: Flip Flop
·
Standards addressed:
·
Standards addressed:
o
K.OA.A.3, K.OA.A.4, K.OA.A.5,
K.NBT.A.1
o
1.NBT.B.2, 1.OA.B.3, 1.OA.B.4, 1.OA.C.5, 1.OA.C.6
o
2.OA.B.2
·
Materials: Index Cards
·
On the front side (denoted by an F in the top
right corner) of each index card write an addition or subtraction fact. On the
reverse side of each card (denoted by a B in the top right corner), write a
related addition or subtraction fact that would make solving the problem easier
for students. For example, if the front
of the card says 7 + 8, the back would say 7 + 7 plus one more, or 8 + 8 minus
one. This activity is not limited to doubles. A card could also read 9 + 4 on
the front, with the back reading 10 + 4 and one less.
·
Students work with a partner. Each take turns
flashing the F side to their partner. If the student cannot solve the front
problem mentally, he or she can say “flip flop” and the student holding the
card will flip the card to the B side to show the easier related fact.
·
If the student can state the answer to the F
side without using the B problem, he or she receives his or her card plus one
more from the stack. If the student can only answer with the help from the B
side, he or she receives only the card originally shown. If the student cannot
answer any of the problems shown, the original card goes to the bottom of the
stack. It is now the other players turn (adapted from Myers & Thorton, 1977).
With Love,
Elizabeth
Flexer, R. (1986). The power of five: The step before the power of ten. The Arithmetic Teacher, 34(3), 5-9.
Retrieved January 30, 2015, from JSTOR.
Number sense every day. (n.d.). Retrieved February 25, 2015, from http://www.learnnc.org/lp/pages/783?ref=search
Myers, A. C. & Thorton, C. A. (1977). The learning disabled
child—learning the basic
facts. Arithmetic Teacher, 25(3), 46-50.
Van de Walle, J.A. (2003). Elementary & Middle School Mathematics.
Boston, MA: Pearson.
