Second Grade



Second GradeMultiplication and DivisionSection 2: DivisionTable of ContentsTopicSuggested Number of DaysPage No.Part 1: Concrete Division – BearsPart 2: Concrete Division – Circles and RectangleDivision StoriesPart 3: Concrete to Pictorial Division Guided Practice Problems #1-6 1 day (4/9)1 day (4/10)2 days (4/13 – 4/14)26101114Additional Resource:Sharing a Set Equally PowerPoint(MATH_2_A_DIV 2014_RES)Division – Sharing to Make Equal GroupsTEKS 2.6The student applies mathematical process standards to connect repeated addition and subtraction to multiplication and division situations that involve equal groups and shares. The student is expected to:TEKS 2.6Bmodel, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent setsTEKS 2.1Aapply mathematics to problems arising in everyday life, society, and the workplaceTEKS 2.1Buse a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying a solution, and evaluating the problem-solving process and the reasonableness of the solutionTEKS 2.1Cselect tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problemsTEKS 2.1Dcommunicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriateTEKS 2.1Ecreate and use representations to organize, record, and communicate mathematical ideasTEKS 2.1Fanalyze mathematical relationships to connect and communicate mathematical ideasTEKS 2.1Gdisplay, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communicationVocabulary: equal, unequal, equally, share, group, set, division, total Teacher Background In this section, students learn about division as the sharing of a set equally among a number of groups. Again, the use of manipulatives is very important in developing a deep and meaningful understanding of division. In Part 3, students continue to bridge from the concrete to the pictorial as they use manipulatives while creating a pictorial representation of their work. Part 1: Concrete Division---Bears19050203200Note: If necessary, quickly review the meaning of equal groups with the slide show or pictures (MATH_2_A_2 MULT 2014_RES) used previously in the Multiplication lesson. 0Note: If necessary, quickly review the meaning of equal groups with the slide show or pictures (MATH_2_A_2 MULT 2014_RES) used previously in the Multiplication lesson. Materials:plastic bearspictures of trees, houses, cars (used in the multiplication lesson)two-color counters “Share a Set Equally” action poster (MATH_2_A_2 DIV POSTER_RES)1.Pass out plastic bears, two-color counters, paper trees, paper houses, paper cars to the students. The teacher creates division stories for the students to act out and discuss. Note: In 2nd grade, the only action learned for division is “Sharing a Set Equally.” Stories should NOT involve the “Taking Away Equal Sets” concept of division. As the teacher tells a division story, the students model it with their manipulatives. For example, the teacher may create a story, such as the one below, about 3 bears and 9 cookies. Plastic bears are used to represent the bears and two-color counters are used for the cookies.Benny Bear brought 9 cookies to eat at lunch time. He wanted to share them with his friends, Bobby Bear and Billy Bear. Benny wanted to make sure everyone got an equal number of cookies so he gave 1 cookie to Bobby, 1 cookie to Billy, and then gave 1 to himself. He continued passing out the cookies, following this type of rotation, until all the cookies were gone. 14668509842500What did Benny Bear want to do with his cookies? share them with his friendsWhat is the total number of cookies Benny had to share? 9How many bears did he share the cookies with? 3 (Bobby, Billy and himself.)How many cookies did Benny Bear get? 3How many cookies did Bobby Bear get? 3How many cookies did Billy Bear get? 3How many cookies did each bear get? 3What do you notice about the number of cookies each bear got? (Elicit the response that they all got an equal number of cookies.)Discuss with the students that 9 cookies were divided into 3 equal groups. How did we make sure each bear got the same number of cookies? (Prompt students to verbalize the action of passing out the cookies to each bear one at a time until there were no more cookies.) You have just divided 9 cookies into 3 equal groups. Each bear received the same number of cookies. Explain to the students that they are dividing when they are putting objects into equal groups. Show them the “Share a Set Equally” action poster (MATH_2_A_2 DIV POSTER 2014_RES) and briefly discuss. Relate to the story about Benny Bear sharing the cookies with his friends. 2.The first story has Benny Bear sharing equally with friends, which is an experience that most students find familiar. To ensure students aren’t misled into thinking that division is done only when you are sharing something with friends, present other stories where division is necessary for the purpose of making equal groups. An example of such a story follows. Students will each need 8 bears and 2 cars to act out this story.One sunny day, 8 bears decided to play baseball in the park. After playing for a while, they got thirsty so they decided to drive to Sonic to buy a drink. They picked up their baseballs, bats and gloves and ran to the first car. (Have students put all the bears by one car.)What do you think will happen if they all tried to get into one car? They will be crowded; they won’t all fit in one car; etc.Can you think of a better way? (If necessary, guide students to the idea of having the bears go in 2 cars.) We have 8 bears and 2 cars. We don’t want to make one car more crowded than the other, so let’s start putting the bears in the cars one at a time. “One for this car, and one for that car”…… (The placement of bears continues in this type of rotation until all 8 bears are in a car.) 14088728572500What did you do with the bears? put them in the carsHow many bears did you have? 8How many cars were there? 2How many bears did you put in the 1st car? 4How many bears did you put in the 2nd car? 4How many bears did you put in each car? 4What is do you notice about how the bears were placed in the cars? (Elicit the response that they are in equal groups.)How did you make your groups equal? (Prompt students to verbalize the action of passing out the bears one at a time into the 2 cars until there were no more bears.) You have just divided 8 bears into 2 equal groups to get 4 bears in each group. At this time, show the students the corresponding number sentence, 8 ÷ 2 = 4. Specifically point out the ÷ sign, and discuss how the two dots make it different from the subtraction symbol. Explain the different parts of the equation. Relate the number sentence back to the story so students can better understand the relationship between the numbers and the details in the story.1752600121920divisionsigndivisionsign 581025283210total(all bears)# of groups (cars)# in each group(bears in each car)00total(all bears)# of groups (cars)# in each group(bears in each car)8 ÷ 2 = 4Revisit the “Share a Set Equally” action poster (MATH_2_A_2 DIV POSTER 2014_RES) and connect the action in the poster to the story of sharing the bears equally among the cars. 3.The teacher tells additional division stories similar to the previous stories which students act out using the paper trees, paper houses and plastic bears. Write and have students explain the division number sentence for each story.4.Interactive Math Notebook (IMN) EntriesRight Side:With teacher guidance, the class writes a division story for the prompt of the 9 flowers and 3 vases (MATH_2_A_3 DIV IMN 2014_RES). Then, the division number sentence is written and discussed. The teacher may wish to write on an anchor chart as the story is created and the number sentence written. It is also beneficial to label the parts of the number sentence with total, # of groups and # in each group as demonstrated on the previous page. The anchor chart may then be posted for future reference.184837412255500Left side:To help them make a personal connection to division, students write about a time they shared something equally with friends or family (MATH_2_A_3 DIV IMN 2014_RES). Write about a time you shared something equally with friends or family. Write the division number sentence for your story.Part 2: Concrete Division– Circles and RectangleMaterials:paper circles (about 8 per student) and paper rectangles (1 per student)two-color countersstudent copies of Division Stories (pg 10)Smartboard Activity (MATH_2_A_4 MULT DIV 2014_RES) “Sharing a Set Equally” action poster (MATH_2_A_2 DIV POSTER 2014_RES)Division Graphic poster (MATH_2_A_5 DIV GRAPHIC 2014_RES)teacher copy of Multiplication and Division Song (MATH_2_A_6 MULT DIV SONG 2014_RES)The plastic bears and pictures are now being replaced with circles (representing the groups), counters for the number in each group, and a large rectangle (representing the total). The students use counters, the circles and the rectangle to act out division stories. The Smartboard activity, MATH_2_A_4 MULT DIV 2014_RES, with circles, “counters” and a rectangle that was used in the multiplication lesson can also be used in conjunction with this section. 1.Display Division Story #1 from page 10. Read the story and insert speed bumps.58102573025There are 12 raisins. There are 3 children. Each child gets the same number of raisins. How many raisins does each child get?00There are 12 raisins. There are 3 children. Each child gets the same number of raisins. How many raisins does each child get?3705225118745213360012255523812503282955218430128270What are we trying to find? number of raisins each child getsPass out the rectangles, the circles and the counters so students can act out the story with you. Remind them that they will continue to use the rectangle to represent the total and the circles to represent the groups like they did with multiplication.Read to the first speed bump. There are 12 raisins. What is happening with the raisins? They are being shared. How many raisins are being shared? 12Do those 12 raisins give us the total, the number of groups or the number in each group? the total Let’s pretend that the counters are raisins. How many counters do we need? We need 12 because there are 12 raisins. Let’s put the counters on the rectangle because the rectangle represents the total number of objects we want to share equally or divide.19716758191500Begin the division number sentence by writing the total number of raisins on the board.220027580010120012Read to the second speed bump. There are 3 children.How many children are sharing the 12 raisins? 3What do the children represent? the groupsWe are dividing the 12 raisins equally into 3 groups.Add the division sign and a 3 to the division number sentence. 159067511176012 ÷ 3 =0012 ÷ 3 =So if the children represent the groups, how many circles do we need? 3(Have students get 3 circles and place them below the rectangle.)124460095885Read to the next speed bump. Each child gets the same number of raisins.Do we need to do anything with our manipulatives? noWe just need to remember that each child gets the same number of raisins.Read to the next speed bump. How many raisins does each child get? To find how many raisins each child gets, let’s pass out the “raisins” (counters) one at a time to the 3 “children” (groups). (Continue to pass out the counters one at a time until there are no more counters left on the rectangle.) 1285875157480Did each child get an equal number of raisins? yesHow do you know? We passed out the same number to each child.How many raisins does each child get? 4Add the answer to complete the division number sentence.140970014160512 ÷ 3 = 40012 ÷ 3 = 4Read the number sentence, “12 divided by 3 equals 4” and have students practice saying it with you. Emphasize to students that the total (12) had been divided by the number of groups (3) to get the number in each group (4). 108585010287012 ÷ 3 = 4total# of groups # in each group12 ÷ 3 = 4total# of groups # in each groupRecord the total, the number of groups and the division number sentence for the first division story (page 10).2.Direct students’ attention to the “Sharing a Set Equally” action poster(MATH_2_A_2 DIV POSTER 2014_RES) and briefly review. Then show students the Division Graphic poster (MATH_2_A_5 DIV GRAPHIC 2014_RES) and post it next to the action poster. How are these two posters the same?If necessary, guide students to see the similarities between the two posters. 3.Teach students the second verse of the “Multiplication and Division Song” (MATH_2_A_6 MULT DIV 2014_RES) and sing together several times. The song is sung to the tune of “Pop! Goes the Weasel.”338137573025Relate this verse to the division graphic.Relate this verse to the division graphic.Look I have the total hereNow I want the small groupsShare the total equallyUsing divisionAlso briefly discuss with students how this verse helps us remember the important ideas about division:We know a total.We know the number of groups. We divide to share the total equally among the groups.4.Partner PracticeUsing the manipulatives (circles, rectangle and counters), have students work with a partner to act out division stories #2-4 on page 10. For each story, students identify the total and the number of groups, and then write the division sentence. Remind students to insert speed bumps as they read the stories. Provide guidance for students as needed.Division Stories1.There are 12 raisins. There are 3 children. Each child gets the same number of raisins. How many raisins does each child get?Total _______ Groups ______Division sentence ______ ÷ ______ = _______2.John has 15 cookies. He puts an equal number of cookies in 3 different bags. How many cookies will be in each bag?Total _______ Groups ______Division sentence ______ ÷ ______ = _____3.There are 12 students. Mrs. Davis divided the students into 4 equal teams. How many students are on each team?Total _______ Groups ______Division sentence ______ ÷ ______ = _______4.Ramiro has 10 Cheetos to share with Cole. He puts them equally on 2 napkins. How many Cheetos does Ramiro put on each napkin? Total _______ Groups ______ Division sentence ______ ÷ ______ = _______Part 3: Concrete to Pictorial DivisionNote: Students continue to use the circles, counters and rectangles as they solve these problems with the 4-step process. They also create a pictorial representation of the manipulatives just as they did in the multiplication lesson.Materials:paper circles (about 8 per student) and paper rectangles (1 per student)two-color counters student copies of Guided Practice Problems #1-6 (pgs 14-19)student copies of Division Partner Practice Problems Part 3(MATH_2_A_7 DIV PARTNER PRACTICE 2014_RES)student copies of Division Independent Practice problems Part 3(MATH_2_A_8 DIV IP 2014_RES) 1.Display Guided Practice Problem #1 (page 14). Read the problem together and insert speed bumps. 10477506985Nathan has 16 pennies. He puts the pennies into 4 equal stacks. How many pennies are in each stack?00Nathan has 16 pennies. He puts the pennies into 4 equal stacks. How many pennies are in each stack?280035051435004371975463550016192506096000Discuss and record the main idea: # pennies in each stack Read to the first speed bump. Nathan has 16 pennies. What does the number 16 tell us? the total number of pennies How do you know?Let’s put down the rectangle because that is where we will put the total number of pennies. Now place 16 “pennies” (counters) on the rectangle.Draw a rectangle in Step 2 and write the number 16 on the rectangle to represent the 16 pennies.-10477513589016# pennies in each stack emanipulatives16# pennies in each stack emanipulativesRead to the next speed bump. He puts the pennies into 4 equal stacks. In this problem, what are the groups? the stacks What do we use for groups? circlesHow many circles do we need? 4 because he is making 4 stacks (groups) of pennies (Place the 4 circles below the rectangle, and then draw the circles below the rectangle in Step 2.)-438150230505manipulatives16# pennies in each stack emanipulatives16# pennies in each stack eRead to the last speed bump. How many pennies are in each stack?(Place a ? in one of the circles.) To find how many pennies are in each stack, we have to divide the 16 pennies equally among the groups.Let’s divide the “pennies” (counters) into 4 groups by passing them out one at a time. (Have students divide the counters onto the circles one at a time.)In Step 2, let’s draw lines to show that we are sharing the total equally.Now, we have to make a picture of the dividing we did with our manipulatives in Step 3. (Have students draw a rectangle and 4 circles in the strategy section so they can follow along with you as you model.) We are going to use tally marks for our counters. (Put a tally mark in each circle “one at a time” as you count to 16 as illustrated below.)2009775736601616Do we have equal groups? yesHow many counters are on each circle? 4What do the circles represent? stacksSo, how many pennies are in each stack? 4The division number sentence is also written in Step 3. Tell students that the answer in division is known as the “quotient”.49530095250Note: In second grade, we introduce the word quotient, which names the answer in division. However, students will not be responsible for memorizing its meaning.00Note: In second grade, we introduce the word quotient, which names the answer in division. However, students will not be responsible for memorizing its meaning.In Step 4, write how the problem was solved. An example of the completed windowpane is shown below.-152400186055Having the total written in the rectangle helps remind students when to stop sharing.# pennies in each stack e16?Divided 16 pennies into 4 equal groups16 ÷ 4 = 4 16Having the total written in the rectangle helps remind students when to stop sharing.# pennies in each stack e16?Divided 16 pennies into 4 equal groups16 ÷ 4 = 4 162.Continue with Guided Practice Problems #2 – 6 found on pages 15 – 19. Some of the problems may be used for partner practice if so desired. Items in these practice problems are objects that can be found in the classroom so the teacher may wish to have them available for students to use when working.3.Partner PracticeHave students work with a partner to complete Division Partner Practice Problems Part 3(MATH_2_A_7 DIV PARTNER PRACTICE 2014_RES). These problems may also be used in small-group instruction situations. If desired, the problems may be placed in page protectors to provide variety and novelty. 4.Independent PracticeStudents complete Division Independent Practice Problems Part 3 (MATH_2_A_8 DIV IP 2014_RES) independently. Have manipulatives available for students to use. 5.Additional ResourceThis PowerPoint (MATH_2_A_DIV 2014_RES) may be used for small-group instruction, warm-ups, etc.Guided Practice Problem #1Nathan has 16 pennies. He puts the pennies into 4 equal stacks. How many pennies are in each stack?304800134620005791200-14732000Guided Practice Problem #2Mrs. Wells has 15 library books to put in 3 tote trays. If she puts an equal number of books in each tote tray, how many books will one tote tray have?22860017780000Guided Practice Problem #3Mrs. Stone has 24 markers to pass out to 4 tables. If she gives each table the same number of markers, how many markers will each table get? 4953001206500Guided Practice Problem #4Henry has 16 erasers to put into 2 bags. If he puts an equal number of erasers in each bag, how many erasers will each bag have? 323850635000Guided Practice Problem # 5Mrs. Banks has a bag of 20 pattern blocks to share equally with 5 students. How many blocks does every student get?3048007112000Guided Practice Problem # 6Dalia has 18 stickers to decorate 3 sheets of paper. If she puts an equal number on each page, how many stickers can she use to decorate each page?19050034925000 ................
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