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Second Grade Multiplication and Division Section 3: Mixed Multiplication and Division Table of Contents Topic Suggested Number of Days Page No. Part 1: Comparing Multiplication and Division Guided Practice Problem #1 (Multiplication) Guided Practice Problem #2 (Division) Guided Practice Problems #1 and #2 Together Part 2: Identifying the Operation Part 3: Solving Problems 1 day (4/15) 1 day (4/16) 6 days (4/17 – 4/24) 2 8 9 10 11 12 Additional Resource: Enrichment Activity (MATH_2_H_MIXED MULT DIV 2014_ENR) Property of Cy-Fair ISD Elem. Math Dept. (2 nd Grade) 2014-2015

Transcript of MIXED MULTIPLICATION AND DIVISION - Pearson Schoolstorage.schoolnet.com/cfisd/MATH_2_A_1 MIXED MULT...

Second GradeMultiplication and Division

Section 3: Mixed Multiplication and Division

Table of ContentsTopic Suggested Number of Days Page No.

Part 1: Comparing Multiplication and DivisionGuided Practice Problem #1 (Multiplication)Guided Practice Problem #2 (Division)Guided Practice Problems #1 and #2 Together

Part 2: Identifying the Operation

Part 3: Solving Problems

1 day (4/15)

1 day (4/16)

6 days (4/17 – 4/24)

28910

11

12

Additional Resource:Enrichment Activity (MATH_2_H_MIXED MULT DIV 2014_ENR)

Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015

Mixed Multiplication and Division

TEKS 2.6 The 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 2.6A model, create, and describe contextual multiplication situations in which equivalent sets of concrete objects are joined

TEKS 2.6B model, create, and describe contextual division situations in which a set of concrete objects is separated into equivalent sets

TEKS 2.1A apply mathematics to problems arising in everyday life, society, and the workplace

TEKS 2.1B use 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 solution

TEKS 2.1C select 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 problems

TEKS 2.1D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate

TEKS 2.1E create and use representations to organize, record, and communicate mathematical ideas

TEKS 2.1F analyze mathematical relationships to connect and communicate mathematical ideas

TEKS 2.1G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

Vocabulary: multiply, multiplication, times, equal groups, unequal groups, total, set, multiplication sentence, repeated addition, amount,

product (exposure only), exactly, division, divide, dividing, separate, division sentence, quotient (exposure only), share

equally

Teacher Background

In this section, students review multiplication and division separately and then compare the two types of problems to pinpoint certain characteristics of each. This insight aids them in deciding between multiplication and division when solving problems. Many opportunities and activities are provided for problem-solving practice. The use of manipulatives

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continues to be extremely important. Our goal in second grade is a meaningful, concrete understanding of multiplication and division. Part 1: Comparing Multiplication and Division

Materials: paper circles and rectangles (as used in the multiplication and division sections)

two-color countersstudent copies of Guided Practice Problems #1 and #2 (pgs 8-9)student copies of the IMN Resource

(MATH_2_A_2 MIXED MULT DIV IMN 2014_RES)

1. Multiplication

Display Guided Practice Problem #1 from page 8. Read the problem together and insert speed bumps.

Discuss and record the main idea: # pieces of paper need

Read to the first speed bump. Mrs. Klein has six tables in her classroom.

What do the tables represent? They are the groups.Let’s put down 6 circles for the 6 tables.Now let’s draw 6 circles in the details/known section (Step 2).

Read to the next speed bump. She gives each table four pieces of construction paper.

What does that tell us? the number in each groupWhat should we put in each circle? 4 counters for the 4 pieces of paper(Put 4 counters in each of the circles.)

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Mrs. Klein has six tables in her classroom. She gives each table four pieces of construction paper. How many pieces of paper does she need?

manipulatives # pieces of paper need

Also, let’s write a 4 in each of the circles in Step 2.

What can you tell me about these groups? They have the same number. They are equal.How do you know they are equal groups?

Read to the last speed bump. How many pieces of paper does she need?

What are we trying to find? the total number of paper neededWe have the groups and the number in each group, and we are trying to find the total. (Place the paper rectangle under the circles with the counters.)

Also, draw the “total” box (rectangle) under our groups in Step 2. Where should we put the question mark? in the rectangle Why? because we want to find the total and the rectangle represents the total.

To find the total, we must combine or put all the groups together. (Move all the counters from the circles to the rectangle.)

In Step 2, let’s draw lines from the circles to the rectangle to show we are putting the groups together into the total.

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4 44 444# pieces of paper needmanipulatives

manipulatives ?

4 44 444

# pieces of paper need

In Step 3, students draw another set of 6 groups and mark 4 tally marks in each. They also write the repeated addition number sentence, 4 + 4 + 4 + 4 + 4 + 4 = 24, along with the multiplication number sentence, 6 x 4 = 24.

In Step 4, students write how the solution was found. An example of the completed windowpane is given below.

2. Division

Display Guided Practice Problem #2 (page 9). Read the problem together and insert speed bumps.

Discuss and record the main idea: pieces of paper each table gets

Read to the first speed bump. Mrs. Klein has 24 pieces of construction paper.

Does the 24 represent the total amount of paper or the groups? the total How do you know? How many counters do we need? 24Let’s count out the 24 counters and put them on the rectangle.Now draw the rectangle in the details/known section and write the number 24 on it.

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Mrs. Klein has 24 pieces of construction paper. She has six tables in her classroom. If she gives each table the same amount, how many pieces of paper will each table get?

?

4 44 444

6 x 4 = 244 + 4 + 4 + 4 + 4 + 4 = 24

Drew 6 groups of 4.Multiplied 6 times 4.

# pieces of paper need

Read to the next speed bump. She has six tables in her classroom.

What do the tables represent? the groupsHow many circles do we need? 6 because Mrs. Klein has 6 tablesLet’s put 6 circles below our rectangle and draw 6 circles below the

rectangle in the details/known section (Step 2).

Read to the next speed bump. If she gives each table the same amount,

What does that mean? She wants to share the total into equal groups.

Read to the last speed bump. how many pieces of paper will each table get?

So, what are we trying to find? the number of pieces of paper at each table or in each group. (Place a ? in one of the circles in Step 2.)What should we do to find how much paper each table gets? share the 24 pieces of paper equally among the 6 tables; divide the 24 pieces of paper so each table gets the same number

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manipulatives

pieces of paper each table gets

24

manipulatives

24

pieces of paper each table gets

Let’s divide the counters into 6 groups by passing them out one at a time.

In Step 3, students then draw six circles and share the 24 equally by making tally marks one at a time in each circle until they reach 24. The tally marks represent the 24 pieces of paper. The division number sentence is also written.

In Step 4, students explain how the solution was found. The completed windowpane is shown below.

3. Comparing Multiplication and Division

Display Guided Practice Problems #1 and #2 together (page 10). Have students look at the work they did when solving these guided practice problems.

What do you see? same names, same itemsWhat do you notice? (Students may give responses that are more specific to the problems. If necessary, summarize for students in more general terms……In the first problem,

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?

24pieces of paper each table gets

manipulatives

24

24 ÷ 6 = 4

?

24

Divided 24 into 6 equal groups of 4

pieces of paper each table gets

we knew the groups and how many in each group, but we were finding the total. In the second problem, we had the total and the number of groups, but we were finding how many were in each group.)

What operation did we use in the first problem? multiplicationHow did you know to multiply? I multiply when I am looking for the total and I know the equal groups with how many each group has.

What operation did we use in the second problem? divisionHow did you know to divide? I divide when I know the total and the number of equal groups, but I am looking for the number in each group.

4. Interactive Math Notebook (IMN) Entry

Right Side:

Sing the entire Multiplication and Division Song with students. Give each student a copy of the song (MATH_2_A_2 MIXED MULT DIV IMN 2014_RES). Have them trim around the song and then glue on the right side of their IMN on the top half of the page.

Together create a flip chart (MATH_2_A 2 MIXED MULT DIV IMN 2014_RES) to summarize what has been learned about multiplication and division. Cut out, cut along the dotted line and fold up the flaps. (The teacher may want to do the cutting beforehand.) Then, glue the shaded portion of the flip chart on the bottom half of the page so that the flaps are still able to open. On the front flaps, record the drawings from Step 2 of the guided practice problems. Under the flaps, record the work from Step 3 of the guided practice problems.

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Guided Practice Problem #1

Mrs. Klein has six tables in her classroom. She gives each table four pieces of construction paper. How many pieces of paper does she need?

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Guided Practice Problem # 2

Mrs. Klein has 24 pieces of construction paper. She has six tables in her classroom. If she gives each table the same amount, how many pieces of paper will each table get?

Guided Practice Problems #1 and #2Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 9

1. Mrs. Klein has six tables in her classroom. She gives each table four pieces of construction paper. How many pieces of paper does she need?

2. Mrs. Klein has 24 pieces of construction paper. She has six tables in her classroom. If she gives each table the same amount, how many pieces of paper will each table get?

Part 2: Identifying the Operation

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Materials: teacher copy of Multiplication/Division Graphic poster(MATH_2_A_3 MULT DIV GRAPHIC 2014_RES)

“Searching for Details” Smartboard Activity (MATH_2_A_4 MIXED MULT DIV 2014_RES)

student copies of Searching for Details Sorting Activity(MATH_2_A_5 MIXED MULT DIV 2014_RES)

manila paper

1. Show students the Multiplication/Division Graphic poster (MATH_2_A_3 MULT DIV GRAPHIC 2014_RES). First review the multiplication picture and discuss with students its meaning. Elicit student help in the explanation. Remind them, if needed, that we are putting together equal groups to find the total in multiplication. Flip the poster and review the division picture. Again, engage students in the explanation. Lead them, if necessary, to conclude that we share a total equally among a certain number of groups to find the number in each group. If desired, refer students to the flip chart in their IMN as a resource.

2. Using the Smart Board activity “Searching for Details” (MATH_2_A_4 MIXED MULT DIV 2014_RES), examine with students the details in various problems---searching for the total, groups and number in each group. Then guide them to connect those details to the operations of multiplication and division.

Read the first problem together and put in the speed bumps.

Have students search for the total. They may use the transparent magnifying glass. If the total is given, circle found. On the blank line, write and label the total. If no total is given, circle missing.

Have students search for the groups. The transparent magnifying glass may again be used. If the groups are given, circle found. On the blank line, write and label the groups. If the groups are not given, circle missing.

Have students search for the number in each group. Again, students may use the transparent magnifying glass. If the number in each group is given, circle found. On the blank line, write and label the number in each group. If the number in each group is not given, circle missing. An example for the first problem is provided below.

2. Examine the details on the remaining slides in the same manner.

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4 people

3 ticket booths

3. Independent Analysis and Sorting

With a partner or independently, students analyze the details in six additional problems (MATH_2_A_5 MIXED MULT DIV 2014_RES). These problems are then sorted into two categories: With Total or Without Total.

Using the six sorted problems, students glue each group on manila paper and draw the pictorial representation for each problem. See picture below.

When the drawings for both categories are completed, have students discuss what they notice. If necessary, point out the relationship between the details present and the operation used to solve each problem. For instance, all problems have equal groups. Division problems have the total and multiplication problems do not. Multiplication problems have both the groups and the number in each group.

Part 3: Solving Problems

Materials: multiplication/division manipulatives (paper circles, rectangles and two-color counters)

station cards, student recording sheets, manipulatives (bear counters, pattern blocks, two-color counters, color tiles) and supplies (crayons and

paper) for Multiplication and Division Stations Activity (MATH_2_A_6 MIXED MULT DIV 2014_RES)

copies of problems from Mixed Multiplication and Division Circuit(MATH_2_A_7A MIXED MULT DIV 2014_RES) for posting

copies of answers from Mixed Multiplication and Division Circuit(MATH_2_A_7B MIXED MULT DIV 2014_RES) for posting

copies of student recording sheets for Mixed Multiplication and Division Circuit(MATH_2_A_7C MIXED MULT DIV 2014_RES)

problem cards, student recording sheets and plastic bears for “Teddy Bear” Small Group Activity (MATH_2_A_8 MIXED MULT DIV 2014_RES)

student copies of Mixed Multiplication and Division Independent Practice Problems Set #1 (MATH_2_A_9 MIXED MULT DIV IP 2014_RES)

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student copies of Mixed Multiplication and Division Independent Practice Problems Set #2 (MATH_2_A_10 MIXED MULT DIV IP 2014_RES)

copies of problems from Mixed Operations Food Circuit(MATH_2_A_11A MIXED OPERATIONS 2014_RES) for posting

copies of answers for posting and copies of student recording sheets for Mixed Operations Food Circuit (MATH_2_A_11B MIXED OPERATIONS 2014_RES)

An assortment of resources are provided for students to practice solving multiplication and division problems with a partner, in small groups, or independently. Use of manipulatives (circles, rectangles and two-color counters) continues in most activities. In some of the activities, these are replaced with other manipulatives (plastic bears, color tiles, pattern blocks, etc.) to add variety. In order to provide a comprehensive review, a resource is also included that contains addition, subtraction, multiplication and division problems. The resources are listed below with a brief explanation and may be completed in any order.

1. Multiplication and Division Stations (MATH_2_A_6 MIXED MULT DIV 2014_RES)

Students work with a partner or in small groups to solve problems at stations. The stations are designed to give students concrete experiences with multiplication and division using a variety of common math manipulatives (plastic bears, pattern blocks, color tiles, etc.). No station is teacher-dependent so the teacher is free to monitor all students. Recording sheets are provided for students to show their work as they solve the problems concretely.

2. Mixed Multiplication and Division Circuit

The teacher may wish to read the book, A Sick Day for Amos McGee, by Philip C. Stead before the students begin the circuit. The problems in the circuit are based on characters from this book. Students may work independently or with a partner to solve the problems using manipulatives as well as the 4-Step Problem-Solving Process. Problems for posting and an illustration for setting up the circuit are found in MATH_2_A_7A MIXED MULT DIV 2014_RES. Answers for posting are found in MATH_2_A_7B MIXED MULT DIV 2014_RES. These answer pages must be cut in half prior to posting. Student recording sheets are found in MATH_2_A_7C MIXED MULT DIV 2014_RES.

3. “Teddy Bear” Small Group Activity (MATH_2_A_8 MIXED MULT DIV 2014_RES)

Students work in a small-group setting to solve problems about teddy bears. They use the multiplication/division manipulatives (circles and rectangle) along with plastic bears as they solve the problems with the 4-step process. A student recording sheet is provided which may be placed in a page protector for repeated use or multiple copies may be run if a student answer booklet is preferred.

4. Independent Practice Problems Set #1 (MATH_2_A_9 MIXED MULT DIV IP 2014_RES)

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Set #2 (MATH_2_A_10 MIXED MULT DIV IP 2014_RES)

Two sets of Independent Practice Problems are supplied. Manipulative use is again encouraged with these problems.

5. Mixed Operations Food Circuit

This circuit provides a review of all operations---addition, subtraction, multiplication and division. All problems are written about food. Problems for posting and an illustration of circuit set-up are given in MATH_2_A_11A MIXED OPERATIONS 2014_RES. Answers for posting and student recording sheets are given in MATH_2_A_11B MIXED OPERATIONS 2014_RES. The answer pages must be cut in half before posting.

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