patterns, relationships, and algebraic thinking

Mathematics TEKS Refinement 2006 – K-5 Tarleton State University

Patterns, Relationships, and Algebraic Thinking Grade 1 Twice the Fun +1

Patterns, Relationships, and Algebraic Thinking

Activity: Twice the Fun + 1 TEKS: (1.5) Patterns, relationships, and algebraic thinking. The student

recognizes patterns in numbers and operations. The student is expected to: (D) use patterns to develop strategies to solve basic addition and

basic subtraction problems; and (1.3) Number, operation, and quantitative reasoning. The student

recognizes and solves problems in addition and subtraction situations. The student is expected to: (A) model and create addition and subtraction problem situations

with concrete objects and write corresponding number sentences; and

(B) use concrete and pictorial models to apply basic and addition facts (up to 9+9=18 and 18-9=9).

Overview: Prior to students beginning work with the Doubles +1 strategy, they must

know the doubles math facts and have learned to model these facts on two ten-frames. The Doubles +1 strategy is then introduced and practiced using the two ten-frame work mats with a step by step approach of building to a mental math level of use. Then the Think Addition strategy is used for the subtraction facts that go with the Doubles +1 facts.

Materials: Double ten-frame workmat for each student

Overhead copy of double ten-frames for teacher—if needed Counters for ten-frame boards: connecting cubes, chips, lima beans… A set of red cubes, chips, or black beans Copy of Twice the Fun +1 Recording Sheet for each student Copy of the My Doubles +1 Math Facts Booklet Copy of Twice the Fun +1 Bridging Recording Sheet Set of Twice the Fun +1 Flash Cards 2 colors of connecting cubes for each student 1 red connecting cube per student Copy of Connecting Cube Recording Sheet for each student Copy of My Doubles + 1 Booklet 2 for each student Booklet 2 Spinner 1 red crayon and 1 black crayon Twice the Fun +1 Dominos Copy of Twice the Fun +1 Domino Recording Sheet

Grouping: small and whole group Time: 30 minutes lessons each day for 3 weeks



Lesson: Procedures Notes 1. Once the children have learned the doubles

math facts they are ready for this strategy. Week 1 Day 1 Build a doubles math fact – do not move the counters to show the total but leave in two sets on two ten-frames. Have children echo the math fact with its sum, all together.

2. After echoing the doubles math fact, example: 6 + 6 = 12, hand students one red cube, red chip, or black bean. Ask them to place the cube/chip/bean on the second ten-frame. Say to the children: “You now have six plus six plus one more, which is equal to thirteen. How can we say this problem with only two addends?” The children should say the new problem is 6 + 7 = 13.

The red color will make it show-up as one more and help the children add one more very easily to the doubles sum.

3. Explain to the children that when two numbers come together on the number line, they are neighbors. When the two numbers are seen in a math fact, we call this a doubles + 1 math fact. Write on the board: 6 + 7 = Have the students determine why 6 + 7 is an example of a doubles +1 math fact.

For example: the relationship between 6 and 7 is that 7 is equal to 6 + 1. Therefore, 6 + 7 = 6 + (6 + 1) = (6 + 6) + 1 (doubles + 1) = 12 + 1 = 13 When students are discussing the doubles +1 problem, they may need to have manipulatives for investigation.

4. Day 2 Continue practicing, but on the second day tie the problems to meaningful word problems to practice forming the problems on the ten-frames. Continue using the same steps to build the problems.

The problems may be teacher or student created and should include everyday experiences and student names.

5. Day 3 Follow the same procedure as on previous

An example of the recording sheet



Procedures Notes days except today you will introduce the ten-frame recording sheet, Twice the Fun +1 Recording Sheet. Build the doubles + 1 math fact on a ten-frame, and say the fact all together. Then show the children how to transfer the fact to the recording sheet.

is found below.

■ ■ ■ ■ ■ ■

■ ■ ■ ■ ■ ■ ■

6. Day 4 Repeat as on previous day except give each child a copy of the My Doubles + 1 Math Facts Booklet. Do two or three pages together bridging from the pictorial model to the abstract. Allow students who are demonstrating understanding to complete the project on their own, but continue to work with those who are still developing an understanding of the strategy and bridging to the abstract. Check the booklet for accuracy. Once completed, the student may take the booklet home to practice reading to an adult for homework.

The book should be assembled so that the double and double +1 face each other. Double 1 ■

■

__ + __ = ___

Double 1 + 1 ■

■ ■

__ + __ = ___

Print booklet front to back using the following sequence. Cover – Double 1 Double 1 +1 – Double 2 Double 2 +1 – Double 3 Double 3 +1 – Double 4 Double 4 +1 – Double 5 Double 5 +1 – Double 6 Double 6 +1 – Double 7 Double 7 +1 – Double 8 Double 8 +1 – Double 9 Double 9 +1 Then cut paper on dotted lines to create two booklets.

7. Day 5 In a small group, the teacher holds up a dot plate arrangement card. The students record the arrangement as a double on the two ten-frames.

This is a mini-assessment to check for student understanding of the concept of double +1.



Procedures Notes Have students complete the bottom ten-frame demonstrating the doubles +1. The students need to record the doubles +1 math fact in the space provided on the Twice the Fun +1 Bridging Recording Sheet.

Teachers should observe how students complete the following: • Do they understand the

concept of double? • Do they demonstrate how to

build the +1? • Can the student bridge from

the pictorial model to the abstract model?

8. Week 2 Days 1 and 2 – Twice the Fun +1 Flash Cards Teacher will hold up two ten-frames that represent double and double + 1. Students read the doubles + 1 math fact and its sum.

It would be good if the doubles +1 card used a red dot as the added dot to reinforce the +1 strategy. This can easily be accomplished by copying the flash cards and adding a red circular sticker. This eliminates having to print the flash in color.

9. Day 3 Give each child ten connecting cubes in two colors plus one red cube (do not use red in the set of ten cubes). Practice building a doubles fact using the two colors of cubes, and then adding the one red cube to the end of one of the sets. Say the math fact all together.

10. Day 4 Again build the doubles + 1 fact, and say it all together. Then show the students how to transfer and record what they built to the Connecting Cube Recording Sheet. Continue until two sheets are completed.

11. Day 5 Give each student a copy of My Doubles + 1 Booklet 2. Today will be an independent practice day. Have the students use the Booklet 2 Spinner. The number that is spun will



Procedures Notes become the double fact being recorded. Example: Instruct if 5 is spun to turn to the page with the 5 at the top. Tell the student to repeat what was done on the previous day by building the fact, saying it, and recording it. Check for accuracy (a grade could be taken if needed), and send home for student to practice reading to an adult as homework.

12. Week 3 Gather materials: Twice the Fun +1 Domino Recording Sheet 1 red crayon 1 black crayon Twice the Fun +1 Dominos

Once the students are able to fluently model and explain how they are solving the doubles +1 math facts through pictorial and symbolic levels, teachers may then use this Doubles +1 domino game. This particular game will build fluency in recognizing doubles +1 math facts and reinforce the mental thinking that occurs to solve the math fact equation.

13. Have students form groups of four. Place dominoes face down in middle of group. Every student selects 1 domino from the group. If the domino is a double (i.e., 5 and 5, 4 and 4, etc.,), then return back to middle of group and select another domino. If the domino is a double + 1 (i.e., 5 and 6, 2 and 3, etc.,), hold your domino vertically with the greater number at the bottom.

This procedure is to ensure that students are able to identify the number that is less. When students record their dominos on the record sheet, the teacher will have an understanding of how the students are processing the strategy. If students are unable to identify the number that is less, difficulty with Doubles +1 strategy will occur. After students demonstrate the understanding of identifying the number that is less, then the dominos may be held in any position.

14. Have students draw, on the record sheet, the Recording the “plus 1” in a red



Procedures Notes dots to match the domino that they have selected. Identify the number that is less on the domino. Record that number on the top and bottom ten-frames using a black crayon. Record the plus 1 onto one of the ten-frames using a red crayon. Your double ten-frames should match your domino. Record the number sentence on the blank record sheet.

color allows the students to create a mental picture for this strategy. Not designating which ten-frame the “plus 1” should go on is important. Students need to have an understanding that it doesn’t matter which number has the “plus 1”. The strategy is still the same whether the plus 1 red dot is on the top ten-frame or the bottom ten-frame. The following is an example of what the recording sheet should look like when it is completed.

15. Continue selecting different dominos and

recording your answers until the record sheet is completed.

Resources: Van de Walle, J.A. (2004). Elementary and middle school

mathematics: Teaching developmentally (5th ed.) Boston, MA:Allyn and Bacon



Twice the Fun +1 Recording Sheet



My Doubles +1 Math Facts Booklet

____________________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - My Doubles +1

Math Facts Booklet



Double 1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 1

__________ + __________ = __________



Double 1 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 1 +1

__________ + __________ = __________



Double 2

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 2

__________ + __________ = __________



Double 2 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 2 +1

__________ + __________ = __________



Double 3

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 3

__________ + __________ = __________



Double 3 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 3 +1

__________ + __________ = __________



Double 4

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 4

__________ + __________ = __________



Double 4 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 4 +1

__________ + __________ = __________



Double 5

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 5

__________ + __________ = __________



Double 5 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 5 +1

__________ + __________ = __________



Double 6

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 6

__________ + __________ = __________



Double 6 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 6 +1

__________ + __________ = __________



Double 7

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 7

__________ + __________ = __________



Double 7 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 7 +1

__________ + __________ = __________



Double 8

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 8

__________ + __________ = __________



Double 8 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 8 +1

__________ + __________ = __________



Double 9

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 9

__________ + __________ = __________



Double 9 +1

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Double 9 +1

__________ + __________ = __________



Twice the Fun +1 Bridging Recording Sheet

_____ + _____ = _______ _____ + _____ = _______

_____ + _____ = _______ _____ + _____ = _______



Twice the Fun +1 Flash Cards



Connecting Cube Recording Sheet

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

__________ + __________ = __________

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

__________ + __________ = __________



My Doubles +1 Booklet 2

____________________

My Doubles +1 Booklet 2



1

__________ + __________ = __________

1

__________ + __________ = __________



2

__________ + __________ = __________

2

__________ + __________ = __________



3

__________ + __________ = __________

3

__________ + __________ = __________



4

__________ + __________ = __________

4

_________ + __________ = __________



5

__________ + __________ = __________

5

__________ + __________ = __________



6

__________ + __________ = __________

6

__________ + __________ = __________



7

__________ + __________ = __________

7

__________ + __________ = __________



8

__________ + __________ = __________

8

__________ + __________ = __________



Booklet 2 Spinner

4

62

7

3

8 5

1

4

62

7

3

8 5

1



Twice the Fun +1

Dominos



Twice the Fun +1 Domino Recording Sheet

patterns, relationships, and algebraic thinking

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