Skills Tested: Addition, Multiplication; Thinking flexibly about how to combine operations.

Materials Needed: photographs of crowds (print me).

Directions:

Explain that sometimes when there is a big event like a concert, we want to know how many people attended. We use photos of crowds.  Scientists do the same thing with populations of animals. We might want to know, for example, how many birds migrated.

Show photo of crowd of people. Ask, how could we estimate how many people are in the photo?

Hand out photos to each group of two students.  They should develop a method for estimating the size in their photo. Partners will record the thinking and all calculations on a white board or sheet of paper.  Students can draw on the photographs they are given.

Each group presents its ideas to other students, and the larger group considers whether the methods seem good.

More extensions / tips for this activity are in the main worksheet (click me)

Credit: Mindset Mathematics Grade 4 by Boaler, Munson, Williams.

Skills Tested: Multiplication, Division; Thinking heuristically about operations.

Materials Needed: game board and cards (print me), one token for each player

Directions:

Draw a card.  Figure out what sign (plus, minus, times, divide) is missing.  If successful, advance your token to the next available sign corresponding to your card.  First player to the finish wins.

Encourage kids to talk through their reasoning for why one operation or another can or cannot work.

Credit: Deceptively Educational

Skills Tested: Multiplication Facts, Factoring

Materials Needed: create worksheet here, pen or pencil

Directions: generate and print a custom worksheet.

Make up or generate a sequence of random numbers within 100 or so (e.g., using dice or cards). For each number, ask the children to look for all factors on their bingo boards.

Works best if students are comfortable with multiplication within 100.

Credit: Tuan Nguyen (source code).

Skills Tested: Representing products as areas. Using different strategies for multiplication.

Materials Needed: Illustration of 24x5, sheet of paper with grid lines, problem bank, and colored markers and sticky notes for each group.

Directions: Students should use colored arrays and equations to construct convincing visual solutions to multiplication problems.

1. Show the visual proof of 24 x 5. Discuss each one and ask students if they can make sense of the problem.

2. Have the students talk with a partner and explain how the visual is showing a solution.

3. Ask the students to share what they have found. What helped them make sense of the proofs? Be sure that they note the use of color as a connection between the pictures and the numbers.

4. Assign each group of students one problem from the problem bank and ask them to make a poster, using a sheet with grid lines, with a visual proof. The proof should include the problem and a drawing with rectangles. Encourage students to use color and to connect the color coding of the rectangles with the math expressions.

5. Have the class discuss each of the posters. Does the class have suggestions on how each poster might be made clearer or easier to understand? Encourage students to put feedback on sticky notes that can be attached to posters.

6. Encourage the groups that made each poster to consider the feedback. Ask them if they'd like to make changes to their posters.

Skills Tested: Representing products as areas. Thinking strategically about what size rectangle would be best at different stages in the game. 

Materials Needed:  4 six-sided dice, One recording sheet per player (click here for the sheet) , One game board per player (print grid) 

Directions:  Students should be able to cover a large area of the game board with rectangles made by summing numbers and multiplying.

1. Players take turns rolling the four dice.

2. Use the numbers shown on the four dice to come up with the length and width of a rectangle.  For example, if a student rolls, 6, 4, 3 and 1, she or he might choose to sum 4 +3 to get a side of 7 and 6 +1 to get another side of 7.  In this case the rectangle would be 7 x 7.  Or the student could sum 6 + 3 to get 9 and 4 + 1 to get 5.  In this case the rectangle would be 9 x 5.

3. Once the student has decided on a rectangle, she draws on it the field.  It can’t overlap any existing rectangle, and it can’t be broken up into smaller pieces.  See the illustration.

4. Label and record. The student labels dimensions on the field and   records the equation on the recording sheet.

5. The players alternate. 

6. Play ends when one player rolls the dice and cannot make any rectangle that will fit on his or her field.

7. To determine the winner, find the total areas covered on each sheet.  The player who has covered the greatest area wins.

Skills Tested: Multiplication by multiples of 10

Materials Needed: 1 die per group of players, 2 large paper clips per group, The game board (click here for board)

Directions:  Students should be able to multiply factors to get four products in a row, column, or diagonal on the game board.

1. Chose which team will uses X’s and which will use O’s.

2. For the first round of play, the opposing team puts a paper clip on one of the factors in the two bottom rows of the game board.  The team that is playing first then places its clip on one of the factors in the other row.  So if the opposing team picks a factor in the row of single-digit factors, the playing team needs to pick a factor that is a multiple of 10.  The playing team multiplies these two numbers, finds their product in the table, and “tops it” by writing its symbol, X or O, on it.

3. The teams now alternate.  On each turn, the playing team moves either one of the paper clips to a new factor, multiplies these factors, and writes X or O on top of the product.

4. The first team to have four X’s or O’s beside each other in a row, column, or diagonal wins.

Tips:

1. Some students may make choices based on facts they know rather than identifying the most strategic factor combinations.  Before students move a clip, ask:  What product would help you the most right now?

2. A team might calculate a product incorrectly.  You might want to have a conversation with the students about what should happen in this case.  One possibility is that the team that made a mistake loses its turn.  Another possibility might be to allow them to make a correction. 

*Adapted from Well Played Grades 3-5 by Linda Dacey, Karen Gartland, & Jayne Bamford Lynch.

Skills Tested: Multiplying fractions by integers. Using the commutative and distributive properties of multiplication

Materials Needed: 1 deck of Equal Values cards per group of four students – (click here for cards) , 1 recording sheet per group – (click here for recording sheet) 

Directions: Students will try to get more pairs of cards that have equal values.

1. To introduce the game, the teacher writes the following expressions on the board and ask students to work with a partner to find two expressions that have the same value. (Examples: ½ x 18, 10 x ½ + 8 x ½, ¼ x 18 + ¼ x 18, 18 x ½)

2. Pairs of students should report back to the larger group their findings and their reasoning.  The class as whole should eventually conclude that all four expressions have the same value. 

3. After explaining the directions and showing how to use the recording sheet, give each team a card with an equal sign.

4. Shuffle the cards.  Deal each team four cards face up for all to see.  Put the other cards facedown in a pile.

5. On each turn, a team can do one of three things:

   • Find two of its card that have an equal value. Set this pack to the side. Replace them with two cards from the top of the pile.

   • Trade one of its cards with one of the other team’s cards when the team is able to make a pack.  Set this pack to the side.  Replace the playing team’s card with a card from the top of the pile.

   • Draw a card from the top of the pile and add it to the team’s cards.

6. When a pack is made, both teams must agree on the value, and then one player records the thinking.  For example, if a team has the two cards 7 x 9 x 1/3 and 3 x 7, they would use the recording sheet to show that both cards equal 21 and they could explain why the two sides are equal.

7. If no cards are left in the deck, a team can still play, but it won’t take a card.

8. The game ends when no team can make another pack.

9. The team with the most packs wins.

Tips: Encourage students who aren’t sure whether expressions are equal to replace larger numbers with smaller numbers and see what they think.  This is an example of simplifying a problem, an important problem-solving strategy. 

What to look for: Do students recognize the commutative and distributive properties of multiplication? 

*Adapted from Well Played Grades 3-5 by Linda Dacey, Karen Gartland, & Jayne Bamford Lynch.

Skills Tested: Multiplication statement identification, multiplication, reflecting on the validity of a multiplication statement

Materials Needed: Individual worksheets from WorksheetWorks

Directions: Distribute the worksheets and have students work on them individually or in pairs. Assigned teachers may provide guided help.

Skills Tested: Working with multiple types of math sentences, including addition and multiplication

Materials Needed: In need of update

Directions: The object of the game is to construct 24 from the numbers on the card. Say, for example, a card contained four numbers: 3, 4, 5, and 5. You may only use each number once. One such solution is: 5 x 5 - 4 + 3 = 24. 

Adapted from 24 game.