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Second GradeMultiplication and DivisionSection 1: Multiplication

Table of ContentsTopic Suggested Number of Days Page No.

Part 1: Equal Groups

Part 2: Concrete Multiplication---BearsPictures of Trees, Houses and Cars

Part 3: Concrete Multiplication---Circles and Rectangle Multiplication Stories

Part 4: Concrete to Pictorial MultiplicationGuided Practice Problems #1-3

½ day (4/2)

½ day (4/2)

1 day (4/6)

2 days (4/7 – 4/8)

2

25

812

1316

Additional Resource:

Put Together Equal Sets PowerPoint(MATH_2_A_MULT 2014_RES)

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

Multiplication – Putting Together Equal Groups

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 2.1A 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, stack, exactly

Teacher Background

In this section, students learn about multiplication as the joining of equal sets. It is extremely important that they develop this understanding concretely with manipulatives. Students must develop a deep comprehension of multiplication in second grade so they have a strong foundation to build upon in later grades. In Part 4, students also learn to bridge from the concrete to the pictorial by simultaneously using manipulatives while making a pictorial representation of their work.

Property of Cy-Fair ISD Elem. Math Dept. (2nd Grade) 2014-2015 1

Part 1: Equal Groups

Materials: slide show or pictures from “Equal Groups or Unequal Groups” (MATH_2_A_2 MULT 2014_RES) for teacher use

1. Hold up the picture or show the slide of the fish in the bowls (MATH_2_A_2 MULT 2014_RES).

What do you see? What do you notice?

Discuss. Point out that there are the same number of goldfish in each bowl. The picture shows equal groups.

What does the word equal mean? equal means the same amount

2. Examine and discuss the other groups of objects from “Equal Groups or Unequal Groups?” (MATH_2_A_2 MULT 2014_RES). Have students explain in complete sentences whether the groups are equal or not equal (unequal). Discuss what changes could be made to make the unequal groups equal.

Part 2: Concrete Multiplication---Bears

Materials: plastic bearspictures of trees, houses and cars for bears (pgs 5-7)“Putting Together Equal Sets” action poster (MATH_2_A_3 MULT POSTER 2014_RES)student copies of IMN Resource (MATH_2_A_4 MULT IMN 2014_RES)

1. Pass out plastic bears, paper trees, paper houses, and paper cars to the students from pages 5-7. The teacher now creates multiplication stories for the students to act out with their manipulatives. Note: In second grade, the only action learned for multiplication is “Putting Together Equal Sets.” Stories should NOT involve the “Rows and Columns” concept of multiplication.

As the teacher tells a multiplication story, the students model it with their manipulatives. For example:

Today is such a bright sunny day that the bears have decidedto climb trees. Have you ever climbed a tree?

There are 4 trees in this part of the park. Put out 4 trees.

Exactly 3 bears decided they would climb each tree. Put 3 bears in each tree. Be careful that they don’t fall out.

How can we find out how many bears are in all the trees? counting the bears; adding the bears; skip-counting by 3


Let’s add the bears and see how many there are.How many bears are in the first tree? There are 3 bears in the first tree. (Write a 3 on the board.)

How many bears are in the second tree? There are 3 bears in the second tree.Let’s make a number sentence out of this situation. (Add another 3 to the first 3 so there is 3 + 3.)Do we have equal groups of bears so far? Yes, there are 3 bears in both of the first two trees.

Now what about the third tree? There are 3 bears in the third tree.(Add another 3 to the number sentence so now there is 3 + 3 + 3.)

We have one more tree to go. What should we do here? Add another 3 for the fourth tree. (Add another 3 to the number sentence so there is 3 + 3 + 3 + 3.)

I need to add all these 3s easily. Does anyone have a suggestion on how we can do that? Students may suggest counting on fingers, skip counting, adding on 3 each time, etc. (Skip count to 12.)

So, 3 + 3 + 3 + 3 = 12. Tell me how many bears are in the trees in a complete sentence? There are 12 bears in the trees.

What do you notice about the number of bears in the trees? (Elicit the response that they were in equal groups.)When we are putting together equal groups of objects, we can get the answer with repeated addition or we can find it faster using multiplication.

Show students the “Putting Together Equal Sets” action poster (MATH_2_A_3 MULT POSTER 2014_RES) and briefly discuss. Relate the poster to the story of the bears and the trees.

At this point, show students the corresponding multiplication equation, 4 x 3 = 12. Explain each part of the equation as outlined below.

4 x 3 = 12

Specifically point out the differences in appearance between the + sign and the x sign.


total(all bears in

the trees)

# in each group

(bears in each tree)

# of groups(trees)

Do NOT show students the commutative property. For example, do NOT show that 4 x 3 is the same as 3 x 4. The picture for 3 x 4 is different than that for 4 x 3, and we do not want to complicate the concept at this early stage.

2. The teacher tells additional multiplication stories which the students act out using the paper trees, paper houses and plastic bears. Write and explain the repeated addition and multiplication number sentences for each story.

3. Partner Practice

Using the paper cars and the plastic bears, have students work with a partner to create their own multiplication story. Both the repeated addition and multiplication number sentences are written for their story. Once stories have been checked for accuracy, allow several students to share their stories with the class to be acted out and discussed by the group.

4. Interactive Math Notebook (IMN) Entries

Right Side:

To summarize what has been learned about equal groups, repeated addition and multiplication number sentences, complete the right-side IMN entry with students(MATH_2_A_4 MULT IMN 2014_RES).

Left Side:

Have students provide examples of an equal group and an unequal group with the left-side IMN entry found in MATH_2_A_4 MULT IMN 2014_RES.


Part 3: Concrete Multiplication---Circles and Rectangle

Materials: paper circles (about 8 per student) and paper rectangles (1 per student)two-color countersteacher copy of Multiplication Stories (pg 12)Smartboard Activity (MATH_2_A_5 MULT DIV 2014_RES) “Putting Together Equal Sets” action poster (MATH_2_A_3 MULT POSTER 2014_RES)Multiplication Graphic poster (MATH_2_A_6 MULT GRAPHIC 2014_RES)teacher copy of Multiplication and Division Song (MATH_2_A_7 MULT DIV SONG 2014_RES)partner copies of “At the Picnic” activity cards and answer sheet(MATH_2_A_8 MULT PARTNER PRACTICE 2014_RES)

The plastic bears and pictures are now 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 multiplication stories. The Smartboard activity (MATH_2_A_5 MULT DIV 2014_RES) has circles, “counters” and a rectangle which can be used in conjunction with this section if desired.

1. Display Multiplication Story #1 from page 12. Read the problem together and insert speed bumps.

Pass out the rectangles, the circles and counters so students can act out the story with you. Read to the first speed bump. There are 3 doghouses in the yard.

Let’s pretend that this circle (show one of the paper circles) is the doghouse. How many circles do we need to show this detail? We need 3 circles because there are 3 doghouses. (Have students put down the 3 circles.)

These doghouses are the groups. We have 3 groups or 3 places where we are going to put the dogs.


There are 3 doghouses in the yard. Each doghouse has 2 dogs. How many dogs are in the yard?

Begin the multiplication sentence.

Read to the second speed bump. Each doghouse has 2 dogs.

Let’s pretend that these counters are the dogs. What should I dowith them? put 2 counters in each circleWhy? There are 2 dogs in each doghouse.(Have students put 2 counters in each circle.)

We have 3 groups – those are the doghouses. We have 2 counters in each group or 2 dogs in each doghouse. We have 3 groups with 2 in each group or 3 groups of 2.

Do we have equal groups?How do you know?

Since we have equal groups and know how many are in each group,what can we do to quickly find the total? We can multiply.

Set up the multiplication sentence.

Read the multiplication expression, 3 groups of 2, to the students.

Read to the last speed bump. How many dogs are in the yard?

To find the total, we have to put all the dogs together. So, let’s move all the “dogs” down to the “Total Box”. (Move all the counters down to the rectangle as shown on the following page.)


# of groups

3

# in each group

# of groups

3 x 2 =

So, how many “dogs” are in the yard? 6 How do you know? because 3 groups of 2 equals 6

Complete the number sentence 3 x 2 = 6 and discuss each part.

Read the number sentence and have students practice saying it, “3 groups of 2 are 6.”

Direct students’ attention to the “Putting Together Equal Sets” action poster(MATH_2_A_3 MULT POSTER 2014_RES) and briefly review. Then show students the Multiplication Graphic poster (MATH_2_A_6 MULT 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.

Teach students the first verse of the “Multiplication and Division Song” (MATH_2_A_7 MULT DIV 2014_RES) and sing together several times. The song is sung to the tune of “Pop! Goes the Weasel”.

Equal groups is what I have,Now I want the total. Put the groups together withMultiplication!

2. Together continue using the manipulatives (circles, counters, and rectangle) to represent the multiplication stories #2-5 on page 12. Teacher and students write and say the corresponding multiplication number sentence for each story. The appropriate repeated addition number sentence is also written.

For each problem worked have students answer the questions:

Do we have equal groups?What are the groups?How many groups are there?What is in each group? (Response contains both object and number of objects.)


# of groups# in each

group total

3 x 2 = 6

Relate this verse to the multiplication graphic.

Then have them write the multiplication number sentence. For example:

3 x 4 = 12

How do we say this number sentence? 3 groups of 4 are 12

3. Partner Practice

Have students work with a partner to complete the “At the Picnic” activity(MATH_2_A_8 MULT PARTNER PRACTICE 2014_RES). Students work together to model the story problem with the manipulatives (circles, counters and rectangle) and then complete the questions on the answer sheet. The answer sheet can be placed in a page protector to conserve paper if desired.

The teacher models how to fill out the answer sheet. For problem #1, the manipulatives and the answer sheet would look like this:

To check for individual understanding, consider keeping one or two of the cards from this activity for students to complete individually.


total# in each group

# of groups

Mother made 6 sandwiches. Each sandwich had 3 pickles on it. How many pickles did Mother use?

Then:

Manipulatives look like this at first:

Multiplication Story #1

There are 3 doghouses in the yard. Each doghouse has 2 dogs. How many dogs are in the yard?


There are 3 party bags with 4 stickers in each bag. How many stickers are there in all?


There are 4 students. Each student has 3 pencils. How many total pencils are there?


There are 5 hot dogs. Each hot dog has 2 pickles with it. How many pickles are there altogether?


John made 3 towers. He put 5 blocks on each tower. How many blocks did he use?


Part 4: Concrete to Pictorial Multiplication

Note: Students continue to use the circles, counters and rectangles as they solve these problems. The students will use the visual of the circles and rectangle to record their details in Step 2 of the problem-solving process.

Materials: paper circles (about 8 per student) and paper rectangles (1 per student)two-color countersstudent copies of Guided Practice Problems #1-3 (pgs 16-18)student copies of Multiplication Independent Practice Problems Part 4 Set #1(MATH_2_A_9 MULT IP 2014_RES)student copies of Multiplication Independent Practice Problems Part 4 Set #2(MATH_2_A_10 MULT IP 2014_RES)

1. Display Guided Practice Problem #1 (page 16). Read the problem together and insert speed bumps.

Discuss and record the main idea. all stars

Read to the first speed bump. There are 3 boxes.

Let’s put down 3 circles for the 3 boxes.What are the boxes? They are the groups.Let’s draw 3 groups in details/known section (or Step 2).

Read to the next speed bump. There are 5 stars in each box.

What is that telling us? That tells us the number in each group.Let’s put 5 counters in each circle.

Also, let’s write a five inside each group in Step 2.


There are 3 boxes. There are 5 stars in each box. How many stars are there in all?

manipulatives all stars

Are the groups equal? yes How do you know they are equal groups?

Read to the last speed bump. How many stars are there in all?

What do we know? There are 3 groups.Do we know anything about the groups? They each have 5 stars.What are we trying to find? the total (Place the rectangle representing the total under the circles with the counters.)

Now, let’s draw the “total” box (rectangle) below our groups in Step 2 and place a question mark in it. Why do you think we want to put the question mark there?

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

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


manipulatives

5 55all stars

manipulatives

?

555all stars

In Step 3, the students show a pictorial representation of their manipulatives by drawing another set of 3 groups and marking 5 tallies in each. They also write the repeated addition number sentence, 5 + 5 + 5 = 15, and the multiplication number sentence, 3 x 5 = 15. Tell students that the answer in multiplication is known as the “product”.

In Step 4, students write how they found the solution. An example of the completed problem is shown below.

2. Additional Guided Practice

Complete Guided Practice Problems #2 and #3 (pages 17-18) with students using the 4-step problem-solving process. Continue using manipulatives and simultaneously drawing a pictorial representation.

3. Partner/Independent Practice

Have students work Multiplication Independent Practice Problems Part 4 Set #1 (MATH_2_A_9 MULT IP 2014_RES) and Multiplication Independent Practice Problems Part 4 Set #2 (MATH_2_A_10 MULT IP 2014_RES) independently using the manipulatives and pictorially recording their work. Depending on the needs of your students, Set #1 may be completed as a partner activity.

4. Additional Resource

This PowerPoint (MATH_2_A_MULT 2014_RES) may be used for small-group instruction, warm-ups, additional guided or partner practice, etc.


Note: In second grade, we introduce the word product, which names the answer in multiplication. However, students will not be responsible for memorizing its meaning.

?

555

I drew a picture.I skip-counted by 5.I multiplied 3 times 5.

5 + 5 + 5 = 153 x 5 = 15

llll

llllllll

all stars

Guided Practice Problem #1

There are 3 boxes. There are 5 stars in each box. How many stars are there in all?



Julia has 4 bags of candy with 2 pieces in each bag. How many pieces of candy are there in all?



Mom put 2 plates on the table. She put 6 brownies on each plate. How many brownies did she put on the plates altogether?


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