Multiplication lesson CAMT 09

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```					       Multiplication
Book: Amanda Bean’s Amazing Dream by Cindy Neuschwander
Brief description: Amanda Bean likes to count. She sees no need to learn to multiply. In
a dream she comes to realize the importance of multiplication.

Alternate books:
My Full Moon is Square by Elinor J. Pinczes
Sea Squares by Joy N. Hulme
Minnie’s Diner by Dayle Ann Dodd
Each Orange Had 8 Slices by Paul Giganti, Jr.

Vocabulary:
Factor                   Array
Product                  Area model of multiplication
Multiply                 Set model of multiplication

Lesson:

Materials:      Amanda Bean’s Amazing Dream
Grid paper
2 facing pages from the book (those showing when book is opened) for
each table/pair of students that show arrays

Procedure:
Discuss the difference in pictures at the bakery (set model) and the
windows ion the houses (arrays – area model).

To reinforce the set model play Circles and Stars game from Marilyn
Burns (or Trains and Boxcars for a more concrete version of the same
game).
Players make a book from 4 pieces of paper. They play 7 games for 1
round and record the results for each game on a separate page in the
book.

Player 1 rolls to find the number of circles he/she will draw. Then player
2 rolls for circles. Player 1 now rolls for the amount of stars that will be
put into each circle. Player 2 follows. They determine who has the most
stars.

Students are asked to “label” their pictures.
The number of circles is listed as the first factor and then the number of
stars is the second factor. The product is the total number of stars.
For example, if a student rolled a 2 and a 3 he would draw two circles and
three stars in each circle.
Under the drawing the student will write 2 x 3 = 6 (2 circles with 3 stars =
6 in all)

Debrief this activity by finding the largest amount of stars, least, discuss
any ties. Draw pictures of problems. See the debriefing chart below.
When you ask students who got the largest product there is usually at
least one student who gets something larger than 36. I will use that as
the largest number I set my chart up for. We can then have a discussion
when we get to it that it is impossible to make that number with regular
6-sided dice.

If a student tells me he/she got 42, I number from 1-42 on the board and
then one by one go through each number – who got this as a product?
What does it look like? Anyone get it a different way?

Variartion: Use a 10 or 12-sided die to produce larger products.

To reinforce the area model have students make array cards from grid
paper. The 1’s, 2’s, 5’s and 10’s can be skipped. At grades 4 & 5 students
may just need to make arrays of facts that are not memorized or are
“shaky.”

Students use pencil to outline arrays and then label the gridded side of
their array with dimensions of the array. Cut out the arrays. On the back
of the array (non- gridded side) they write the product in the center and
lightly write one of the factors of the array and the owner’s initials.

2x6
2
12
6x2                                                cbs

Cards should be store in plastic bags.

Students then can play “War” with their array cards.
Pairs of students play. Each student makes a stack with his/her array
cards, product side down. On each turn the players give the product of
the top card. The player with the greatest product gets both cards. In
case of a tie, the players go to the next card in their stack.

Students can play “I know It” with their array cards. The cards are spread
out with either side facing upward. One player puts a finger on a card (do
not pick it up) and says the answer (either the product - 12 or the facts –
2 x 6). Turn the card over to check the answer. If the player is correct
he/she keeps the card. Students can keep a list of “arrays I know” and
“arrays I’m working on” as they play this game.

Use Amanda Bean’s Amazing Dream to look for sets and arrays.
Give each group a 2-page spread from the book. They are to identify all
arrays or sets on the given pages and duplicate them on their paper. The
students must describe the arrays or sets with the factors as shown
below.

3x4 =12

3x4 = 12

Students are then asked to create 4 new arrays or sets that were not on
their pages.

Class discussion:      Students share their arrays or sets from the smallest (you could
relate to area here with the arrays) to the largest.
List the multiplication facts and have students add these to a
multiplication journal. The journal section can be entitled, “Facts
I’ve Found.”

Literature Connection: Refer to Isle of Immeter – area and perimeter – Inners and Edges game.

Other activities/games:
BUZZ (this could be a “warm-up” activity before the actual lesson

2006 TAKS items:
Grade 3 # 13, 36, 28            Grade 4 # 41, 42, 34             Grade 5 # 43, 3, 12
The Game of Inners and Edges
From Sir Cumference and the Isle of Immeter by Cindy Neuschwander

Materials:     Color tiles

Grid paper

1. Player 1 makes a rectangle from color tiles and states the number of square tiles used –
the inners.

12 inners

2. The first person to count all of the outside edges gets to keep the tiles.

14 edges

3. Players draw a diagram of the color tile configuration giving the # of inners (area) and
the # of edges (perimeter).
4. The person with the most tiles wins.
5. When students repeat the game they need to include the words area and perimeter
with their descriptions of the arrays.

12 inners or an area of 12.

14 edges or a perimeter of 12.

6. Students need to journal about any short cuts they took to find the edges (perimeter).
Did they always count all four edges? Did they multiply one side by 4 for squares? Etc.
BUZZ
Objective: To review multiplication skills
Time: 10-15 minutes
Materials: None
Levels: 3-7
Players: Whole class

1. Have students stand behind desks.
2. Name the multiples being BUZZED.
3. Explain rules. We will count in sequence starting with one, however all multiples of
the chosen number must be BUZZED rather than named. Any number that contains the
BUZZ number as a digit is also BUZZED.
For example: If the 4’s are chosen to be BUZZED, the counting sequence would go as
follows: 1, 2, 3, BUZZ, 5, 6, 7, BUZZ, 9, 10, 11, BUZZ, 13, BUZZ, (14 contains a four), 15,
BUZZ, 17...
If a student says the wrong number, he/she will be motioned to sit down. The next
player must say what the correct response should have been. This can get crazy when
you get to the sequence of numbers that begin with the BUZZ digit. (Like the 40’s in the
example) The last person standing is the winner.
The Tax Collector Game

Gameboards

Object of the game:   To collect the most points.

Procedure:            Explain that one person (the teacher for the demo) will be the Tax
Collector. The class (or other person/team) will be the Tax Payer.
The Tax Payer always picks first. The Payer must give all the factors of
the chosen number to the Tax Collector. Factors and chosen numbers are
crossed off the board. Any numbers chosen that have no remaining
factors are paid to the Collector. The most points win the game.

A Note:               The kids ALWAYS loose the first game. Most times they lose the second
game. I usually play the game with them twice and them out them in
groups of 2 to play each other. I NEVER tell them how to win. They
have to figure it out. I do pull it all together at the end of class to discuss
what they are finding.

Scaffolding

Questions:            Why did you choose the first number?
What is a good first move? Why?
What kinds of numbers are represented on the board? (you’re looking
for prime & composite not odd and even)
Does it matter what the first number is?
What do you want to do differently the next time you play?

1       2        3        4                Payer     Collector

5       6        7        8

9       10       11       12

13      14       15       16

17      18       19       20

Extension:            Increase the board to 24.
1        2        3         4

5        6        7         8

9       10        11        12

13       14        15        16

17       18        19        20

1    2        3         4         5

6    7        8         9         10

11   12       13        14        15

16   17       18        19        20

21   22       23        24        25

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