Number, Operation, and Quantitative Reasoning


 Ophelia Blake
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1 Number, Operation, and Quantitative Reasoning Activity: TEKS: Think Addition (2.3) Number, Operation, and Quantitative Reasoning. The student adds and subtracts whole numbers to solve problems. The student is expected to: (A) recall and apply basic addition and subtraction facts (to18); (B) model addition and subtraction of twodigit numbers with objects, pictures, words, and numbers; (2.5) Number, Operation, and Quantitative Reasoning. The student uses patterns in numbers and operations The student is expected to: (C) use patterns and relationships to develop strategies to remember basic addition and subtraction facts. Determine patterns in related addition and subtraction number sentences (including fact families) such as = 17, = 17, 17 8 = 9, 17 9 = 8. (2.12) Underlying processes and mathematical tools. The student adds applies Grade 2 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: (B) Solve problems with guidance that incorporates the processes of understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness; Overview: A prerequisite for this strategy is for students to know the addition math facts and be able to use the tenframe fluently. According to Van de Walle (2004), subtraction facts prove to be more difficult than addition (p.165). He suggests encouraging students to think What goes with this part to make the total? (p. 165). This approach lays the foundation for the strategy Think Addition. Think Addition requires students to use known addition facts to create the unknown quantity or part. The Think Addition strategy will be developed using the tenframe work mats and used to build a mental recall of the subtraction facts. Materials: Prior to Lesson Card stock/construction paper Roll m Cards master Tape Glue Think Addition Page 1
2 Lesson Tenframe Mat for each student Double Tenframe Mat for each student 10 to 18 Counters for the Tenframes (cubes, colored counters or lima beans) Flap Cards Using Black Dots (week 3) Flap Cards with Missing Addend (week 5) Notebook paper 9sided die Roll m Cards Extension Activities Who Are My Relatives? Who Are My Relatives? Cards Half of Doubles (Pick the cards that best fit the students level of understanding.) I Have Who has? Story Problem Cards I Have Who has?abstract Cards Grouping: Time: Small or whole group This lesson should last 30 minutes each day for several weeks. Much depends on students developmental level and the amount of time designated daily for mathematics instruction. Lesson: Procedures 1. Prior to Lesson Teacher needs to make flap cards. The flap cards rely on the Think Addition strategy. There are two sets of flap cards that need to be made. Students will work in pairs when they use the flap cards. Make enough flap cards so that each pair of students will have each set of flap cards. See the notes for directions for making the flap cards. Notes To make flap cards: Cut out several card stock or construction paper cards (9 x 3 ) and other cards (4 1/2 x 3 1/2 ). Tape the shorter card to the top right side of the larger card. You will make two sets of cards. To make the first set of flap cards: On the long piece of the flap card, write a digit followed by a minus sign. After the minus sign, use black dots to represent the number to be subtracted (subtrahend). Follow the black dots with an = sign and then an empty box. On the fold down flap, place the Think Addition Page 2
3 Procedures Notes answer using black dots. For example: 5 (black dot) = empty box. Answer is represented on fold down flap as four black dots. To make the second set of flap cards: On the long piece of the flap card, write a number (118) followed by a minus sign, and then the number to be subtracted followed by an = sign and an empty box. On the fold down flap, write the numerical answer. For example: 6 4 = empty box Answer is represented on fold down flap as the numerical answer of 2. Duplicate Roll m Cards onto cardstock. 2. Explain to the students that each addition fact has a subtraction fact that is related to it because it uses the same numbers. Students need one week to process the relationships taught in this step. Think Addition Page 3
4 Procedures Write an addition fact up to 10 on the overheard or board. Have students build on tenframe mats the number that is being subtracted (called the part or subtrahend). The students will quickly see how many counters need to be added to make 10 (the whole). Example: For 10 4, the students would build 4 on the tenframe mat. Then ask: How many counters would be needed to equal or make 10? The students should identify that six counters are needed to fill the tenframe, so the answer would be 6. Continue this format for two days. On the third day, begin tying the subtraction facts to word problems for the remaining part of the week. Have the children work out the word problems on their double tenframe mats as you read or say the word problems orally. Notes Example: = 10 and show how it is related to 10 4 and Explain each math fact is composed of 2 parts and the sum or total of the parts. Another name that mathematicians use for the sum or total is whole. Our class is part boys and part girls but the whole class includes both groups or both parts (boys and girls). When we subtract, we begin with the whole group number and must find the part that remains after a part was removed or show how the two numbers compare to one another to find the difference between them. Minuend is defined as the number from which another number is to be subtracted (Lexico Publishing Group, 2006). Subtrahend is defined as the number being subtracted (Lexico Publishing Group, 2006). 10 Minuend  4 Subtrahend 3. Give each student a tenframe mat, 10 counters, and a tenframe recording sheet. a. Teacher writes a subtraction fact under the first tenframe on the recording sheet. b. Have the students copy it. c. Students build the number being subtracted on their tenframe mats. d. Have students transfer what is on the tenframe mat to the recording sheet. e. Next draw a small x in each box needed to make the total or sum. f. Record the number of x s it took to fill the tenframe to match the fact written under the tenframe. g. State the subtraction math sentence Students need to spend about 1 week developing this portion of Think Addition. As the students are building the subtraction fact on their tenframe mats, the teacher should also be modeling the procedure. This can be demonstrated on the overhead or document camera. Be sure to model how to transfer what is on their mat to their tenframe recording sheet. Continue modeling this through out Think Addition Page 4
5 Procedures including its difference. h. Then have students echo what you have just said. For example, use the subtraction fact Students would build the number 4 on the tenframe. Next, they would write six x s on the mat to complete the tenframe. The students would say the subtraction sentence... 4 and 6 are 10 so 10 minus 4 equals 6. Notes the week. When you see students are beginning to fill in the tenframe with the missing part on their own, allow them to complete the activity independently. Continue working with other students until they too reach this independent level of understanding. 4. Create Think Addition Flap Cards. Prior to teaching this part of the lesson, make two sets of Think Addition Flap Cards as directed in Step Hold a flap card open so students see the math fact with the missing addend box (a question mark is drawn inside the box). Once an answer is given, fold the flap down so students can see the answer. Model how to write the problem horizontally. For example: 6  =? This part of the lesson should be conducted in small groups of three or four students. While working with the small group, other students are rotating through mathematics centers that contain activities that review previously taught concepts. The centers should be developmentally appropriate, handson, and studentindependent activities. After the initial introductory lesson, place the flap cards into centers for students to practice daily. If the student cannot quickly give the answer to the missing addend of an addition math fact, use a tenframe for the student to fill in with the number of dots uncovered on the long card. Then ask, How many more dots do you need to place in the tenframe to make the first number (minuend)? Think Addition Page 5
6 Procedures Notes 6  = 6 4 = 2 On day two, split all the students into pairs and have the students use the cards to challenge each other. Have students write the subtraction sentences on notebook paper. After students have had time to practice with the previous cards. Introduce the abstract cards in the same fashion. Students work can be used for formative assessment to determine how long students need to continue work with the flap cards. 6. Once students have mastered subtraction facts through 10, introduce cards with facts through 18 following the same procedures as before. 7. Roll m 1. Place number cards (10 18) face down and 9sided die in middle of group. 2. Begin by rolling the nine die, and then all participants build the number rolled on the tenframes. 3. Next, turn over one number card and begin thinking addition. 4. The participant who flipped the number card will ask the group, (# on die) and what makes (# on card)? (Example: 5 and what makes 13? 5. Record subtraction fact onto notebook paper. 6. Continue playing until everyone has worked 10 problems. This activity would be excellent as a baggie game to send home for students to work on with their parents. They would return the recorded subtraction problems as their homework. Think Addition Page 6
7 Homework: Assessment: Extensions: The activities used each week can be sent home as homework so that students can practice with an adult or older brother/sister. Each day, the teacher should assess which students understand the concept being taught and which may need additional tutoring time. A final assessment should include the following: Can a student give the missing math sentence when they are given three fact family math sentences? Can a student give the missing addend to an addition and subtraction math fact? Since Think Addition is the only lesson submitted for learning the subtraction facts, some additional ideas have been included for practicing the facts. Who Are My Relatives? (played similar to I have Who has?) a. Duplicate on cardstock the Who Are My Relatives? Cards. b. To play the game, distribute cards to students. c. Have a student begin by reading, the family? d. Four students holding the cards with their family should go to the front of the class. e. Each person reads his/her answer. Then together, they read the question on the card. f. The students remain standing until the game is complete. g. Play continues in the same manner and at the end of the game a circle will be formed with all members of the class forming the circle. Half of Doubles Pick from the two sets of I have Who has? Cards that best fits the level of understanding for your class. a. Divide the students into group of three. b. To play the game, distribute cards to students. c. Have a student begin by reading the question at the bottom of the card. d. The students holding the card should go to the front of the class. e. One of the students from the group reads his/her answer. Then together, they read the question on the card. f. The students remain standing until the game is complete. g. Play continues in the same manner and at the end of the game a circle will be formed with all members of the class forming the circle. Students can create other cards so that the game changes each time they play, increasing their learning of the facts. Think Addition Page 7
8 Resources: Lexico Publishing Group. (2006). Dictionary.com. Online at Van de Walle, J.A. (2004). Elementary and middle school mathematics: Teaching developmentally (5 th ed.) Boston, MA:Allyn and Bacon Modifications: You may need to give students an empty tenframe mat to use for some of the activities or tape a small empty tenframe on student desks to encourage students to use a tenframe when working out math facts and to help lead to a mental image of the numbers. Think Addition Page 8
9 Who Are My Relatives? Cards I am = 5 I am = 5 the 8 family? I am 5 3 = 2 the 8 family? I am 52 = 3 the 8 family? I am = 8 the 8 family I am = 8 the 9 family? I am 8 2 = 6 the 9 family? I am 8 6 = 2 the 9 family? the 9 family? Think Addition Page 9
10 I am = 9 I am = 9 the 6 family? I am 9 5 = 4 the 6 family? I am 9 4 = 5 the 6 family? I am = 6 the 6 family? I am = 6 the 10 family? I am 6 5 = 1 the 10 family? I am 61 = 5 the 10 family? the 10 family? Think Addition Page 10
11 I am = 10 I am = 10 the 7 family? I am 10 2 = 8 the 7 family? I am 10 8 = 2 the 7 family? I am = 7 the 7 family? I am = 7 the 5 family? I am 7 3 = 4 the 5 family? I am 7 4 = 3 the 5 family? the 5 family? Think Addition Page 11
12 I Have Who Has. Story Problem Half of Doubles Cards I have 5. We planted 18 flowers in our school garden. The weather was so hot, that onehalf of our flowers died. Who has how many flowers are still growing in our garden? I have 9. Our neighbors have 8 dogs and cats. Onehalf of the animals are dogs. Who has how many cats my neighbors have? I have 4. My mom bought a dozen of eggs. She tripped coming into the house and only 6 eggs were not broken. Who has how many eggs were broken? I have 6. Our car has 4 tires. My uncle drove over a nail in the street and onehalf of the tires went flat. Who has how many tires are not flat? Think Addition Page 12
13 I have 2. My grandmother gave me $16. She asked me to share onehalf of the money with my brother. I have 8. A pie was cut into 6 pieces. I ate onehalf of it. Who has how much money I was suppose to give to my brother? Who has how many pieces I ate? I have 3. I have 7. I went to summer camp for 2 weeks. It rained onehalf of the days I was there. My father bought a pair of soccer shoes. 1 of the shoes did not have shoestrings. Who has how many days it rained at camp? Who has how many shoes did not have shoestrings? Think Addition Page 13
14 I have 1. Our class filled 10 boxes with cans to recycle. Our teacher took onehalf of the boxes to get recycled. Who has how many boxes did not get recycled? Think Addition Page 14
15 I Have Who Has Abstract Half of Doubles Cards I have 1. I have 9. Who has 2 1 of 18? Who has 2 1 of 8? I have 4. I have 6. Who has 2 1 of 12? Who has 2 1 of 4? Think Addition Page 15
16 I have 2. I have 8. Who has 2 1 of 16? Who has 2 1 of 6? I have 3. I have 7. Who has 2 1 of 14? Who has 2 1 of 2? Think Addition Page 16
17 Roll m Cards Think Addition Page 17
18 Think Addition Assessment Student Name Can a student give the missing math sentence from 3 fact family math sentences given? Can a student give the missing addend to an addition and subtraction math fact? Think Addition Page 18
19 Tenframe Mat Think Addition Page 19
20 Name Tenframe Recording Sheet Think Addition Page 20
21 Double Tenframe Mat Think Addition Page 21
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