🎯Making Connections: Introduction to Multiplication as Repeated Addition

Lesson plan

Objectives

• Identify multiplication as the total number of objects in equal groups.
• Write a repeated addition equation to represent a visual model of equal groups.
• Convert a repeated addition equation into a multiplication equation using the 'x' symbol.
• Interpret the first factor as the number of groups and the second factor as the size of each group.

Materials

• Small counters or buttons (20 per student)
• Individual whiteboards and dry-erase markers
• Chart paper with pre-drawn 'Equal Groups' vs 'Unequal Groups'
• Visual anchor chart showing: Groups x Size = Total
• Student math journals
• Large foam dice for the activity

Warm-up

Begin by asking students to stand up and form groups of 3 around the room. Once grouped, ask the class, 'How can we quickly find the total number of fingers in one group?' Then, ask how we could find the total for the whole class without counting one by one. Write their suggestions on the board, specifically highlighting 5 + 5 + 5... as a strategy. Explain that today we will learn a 'math shortcut' for adding the same number over and over again.

Direct instruction

1. Define 'equal groups' as groups that have the exact same number of items inside them. Show a picture of 3 plates with 4 cookies each.
2. Demonstrate writing a repeated addition sentence for the cookies: 4 + 4 + 4 = 12.
3. Introduce the multiplication symbol (x) and explain it means 'groups of'. Write 3 x 4 = 12 on the board.
4. Explicitly label the parts: The 3 represents the number of groups (plates), and the 4 represents the size of each group (cookies).
5. Show a non-example: 2 plates with 3 cookies and 1 plate with 5 cookies. Ask students if we can use our multiplication shortcut here (No, because the groups are not equal).
6. Model drawing an array: 2 rows of 5 dots. Show how this is 2 groups of 5, or 5 + 5, which equals 2 x 5 = 10.
7. Practice 'Think-Pair-Share': Show 4 baskets with 2 apples. Have students whisper the addition sentence to a partner, then the multiplication sentence.

Guided practice

Distribute 12 counters to each student. Guide them to create 4 groups of 3 counters each. Walk through the process of writing the addition sentence on whiteboards (3 + 3 + 3 + 3 = 12). Then, guide them to translate this to multiplication: 4 groups of 3 is 4 x 3 = 12. Repeat the process with 2 groups of 6. Worked Example: For 3 groups of 5, we write 5 + 5 + 5 = 15. Since there are 3 fives, the multiplication is 3 x 5 = 15.

Independent practice

Students will complete a 'Matching Models' worksheet where they must draw lines connecting visual groups (e.g., 5 clusters of 2 stars) to the corresponding repeated addition sentence (2+2+2+2+2) and the final multiplication equation (5 x 2 = 10). They will then create two of their own models and write the equations below them.

Closure

Review the key vocabulary: factor and product. Ask the class to show on their fingers: 'If I have 3 groups of 2, what is my total?' Exit Ticket Prompt: Draw 4 circles with 3 dots in each circle. Write one addition sentence and one multiplication sentence to show the total number of dots.

Assessment

Mastery will be measured by the Accuracy of the Exit Ticket (100% required for 'mastered'), performance on the 10-question worksheet, and the ability to correctly identify factors during the guided practice observation.

Differentiation

For struggling learners: Provide 'sentence frames' for equations ( __ + __ = __ ) and physical plastic hoops to visually separate groups of counters. For advanced learners: Introduce the 'Commutative Property' by asking if 3 x 4 gives the same total as 4 x 3, and have them prove it using a drawing.

Mastering Equal Groups

For each problem, look at the picture or description. Write the repeated addition sentence, then write the multiplication sentence.

1. Draw 3 groups of 5 stars.
2. There are 4 nests. Each nest has 2 eggs. How many eggs in total?
3. Write the multiplication sentence for: 6 + 6 + 6 =
4. Write the multiplication sentence for: 10 + 10 + 10 + 10 + 10 =
5. Draw an array with 2 rows and 4 columns.
6. A tricycle has 3 wheels. How many wheels do 5 tricycles have?
7. Convert to multiplication: 7 + 7 =
8. There are 6 ladybugs. Each ladybug has 6 legs. Write the equation.
9. 3 + 3 + 3 + 3 + 3 + 3 + 3 = 21. Write this as multiplication.
10. Create your own equal groups drawing for 4 x 4.

Introduction to Multiplication Quiz

1. What is another way to write 2 + 2 + 2 + 2 + 2?
   • 2 x 2
   • 5 x 2
   • 2 x 4
   • 5 + 2
   Answer: 5 x 2
2. In the equation 3 x 4 = 12, what does the '3' represent?
   • The total
   • The size of each group
   • The number of groups
   • The sum
   Answer: The number of groups
3. Which of these is NOT an equal group?
   • 3 bags with 2 candies each
   • 4 boxes with 5 toys each
   • 2 plates with 3 cookies and 4 cookies
   • 5 piles with 1 book each
   Answer: 2 plates with 3 cookies and 4 cookies
4. What is the product of 4 x 3?
   • 7
   • 1
   • 12
   • 15
   Answer: 12
5. How would you write '6 groups of 5' as multiplication?
   • 6 + 5
   • 5 x 6
   • 6 x 5
   • 6 - 5
   Answer: 6 x 5
6. If you have 0 groups of 5, how many do you have total?
   • 5
   • 0
   • 1
   • 10
   Answer: 0
7. Which addition sentence matches 2 x 9?
   • 9 + 9
   • 2 + 2
   • 2 + 9
   • 9 + 2
   Answer: 9 + 9
8. An array has 3 rows of 10. What is the total?
   • 13
   • 30
   • 20
   • 33
   Answer: 30

Home Connection: Multiplication Hunt

This week we are starting multiplication! Instead of just memorizing facts, we are learning that multiplication represents equal groups in the real world. Please help your child find items around the house that come in equal groups to complete the tasks below.

• Find an item in the kitchen that comes in equal groups (e.g., an egg carton) and write the repeated addition sentence.
• Draw a picture of 4 cars and count the total number of wheels using multiplication.
• Solve: 5 + 5 + 5 + 5 = ___ and write the matching multiplication sentence.
• Find a pack of juice or soda. How many are in one pack? If you had 2 packs, how many would you have?
• Draw 6 circles. Put 2 'seeds' in each circle. Write the multiplication equation for your drawing.
• Explain to a family member the difference between '3 + 3' and '3 x 3'.

Vocabulary

Multiplication · noun

An operation used to find the total number of items in equal groups.

"We use multiplication to count the legs on five dogs quickly."

Equal Groups · noun

Groups that have the same number of objects.

"Three boxes with four pencils each are equal groups."

Factor · noun

A number that is multiplied by another number.

"In the problem 2 x 3, both 2 and 3 are factors."

Product · noun

The answer to a multiplication problem.

"The product of 5 times 2 is 10."

Repeated Addition · noun

Adding the same number again and again.

"4 + 4 + 4 is repeated addition."

Array · noun

A set of objects arranged in equal rows and columns.

"The muffins in the tin formed a 3 by 4 array."

Row · noun

Objects arranged in a horizontal line (across).

"The first row of the classroom has five desks."

Column · noun

Objects arranged in a vertical line (up and down).

"The columns of the building were very tall."

Equation · noun

A mathematical statement showing that two expressions are equal using an equal sign.

"2 x 5 = 10 is a multiplication equation."

Symbol · noun

A sign used to represent an operation, like 'x' for multiplication.

"The multiplication symbol looks like a slanted cross."

Activities

• Roll a Group · 10 minutes

  Students work in pairs with two dice. The first student rolls to determine the 'Number of Groups.' The second student rolls to determine the 'Size of Each Group.' Both students draw the model on their whiteboards and write the multiplication sentence. For example, if they roll a 3 and a 4, they draw 3 circles with 4 dots in each.

• Human Arrays · 10 minutes

  The teacher calls out a multiplication fact, such as '2 times 5.' Students must quickly move to organize themselves into an array with 2 rows and 5 students in each row. The 'extra' students act as 'inspectors' to check if the rows and columns are straight and equal before switching roles.

• Gallery Walk: Equal or Not? · 10 minutes

  Place 8 large images around the room showing various groups of objects (some equal, some unequal). Students walk to each station with a clipboard and mark 'Yes' or 'No' for whether it represents multiplication. If 'Yes,' they must write the Equation. If 'No,' they explain why (e.g., 'One group has 5, the others have 4').

• Counters Relay · 15 minutes

  Divide the class into teams. The teacher shows a repeated addition sentence on the screen (e.g., 7 + 7 + 7). One student from each team must run to their station, build the model with counters, and write the product on a card. The first team to correctly model and solve the equation wins a point for that round.