Lesson 8

The purpose of this Number Talk is to elicit strategies and understandings students have for multiplying ​​one- and two-digit numbers, which will be helpful later in this lesson when students multiply within 100.

When students use products they know to find a product they don’t know, they look for and make use of structure (MP7).

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

• “How did the first 3 expressions help you find the value of the last expression?” (The last expression is 17 groups of 4 which is like 10 groups, 5 groups, and 2 groups of 4 combined. Adding up the value of the first 3 expressions gives you the value of the last expression.)

In this activity, students check their progress toward fluent multiplication within 100. They do this by revisiting an activity from a previous unit, in which they sorted multiplication expressions from \(1 \times 1\) to \(10 \times 10\) into groups: those that they know right away, those they can find quickly, or those they don’t know yet. Here, students sort the same set of expressions, then practice finding five products of their choice after sharing strategies for finding products they don't know yet.

• Gather materials from Multiplication Card Sort, an activity from a previous unit.
• If remaking the cards, create a set of cards from the blackline master for each group of 2.

• Groups of 2
• “Today we’re going to revisit the multiplication facts to see how many you’ve learned so far.”
• “There are some multiplication facts you know right away. What does it mean to ‘know something right away?’” (To know it without doing much thinking. To know from memory.)
• “There are some multiplication facts you may not know right away but can find quickly. What do you think it means ‘to find a product quickly?’” (To figure it out within a few seconds, using a strategy.)
• Consider asking:
  • “Does anyone have different ideas about what it means to find a product quickly?”
  • “Can someone give an example of a strategy for finding a product quickly?”
• Give each group a set of cards and a copy of the table from the blackline master.

• “Take some time to quiz each other on your multiplication facts. Use the table to sort the expressions into three groups based on whether your partner knows the value right away, can find the value quickly, or doesn't know it yet.”
• 7–10 minutes: partner work time
• “Choose five expressions whose value you don’t know yet and record them. These are the products you will practice finding.”
• 1 minute: independent work time
• “Now, share the products you want to practice with your partner. Work together to think of some strategies you could use to remember or find their values quickly. After you have some ideas, practice finding the products you chose.”
• 5–7 minutes: partner work time

If students are not sure what strategy could help them find multiplication facts, consider asking:

• “Is there a multiplication fact that you know that could help you with this fact?”
• “Is there another group you could ask about a strategy for the fact you're working on?”

• “What were some useful strategies for finding products you didn’t know yet?” (Using a product I already know to find the one I didn’t know yet. Using products of 2, 5, and 10 to figure out other products.)

The purpose of this activity is for students to learn stage 3 of the Compare center to practice multiplying within 100. Students may compare expressions by finding the value of each or by reasoning about the features of the expressions (MP7). (For example, when comparing \(12\times7\) and \(12\times9\) they see that both involve 12 groups but in \(12\times9\) there are 2 more in each group than in \(12 \times 7\).)

When students multiply 2 one-digit numbers, they should know these products from memory. When students multiply a one-digit and a two-digit number, students should have an efficient method for finding the product, but do not need to know the product from memory. If students need more practice with their one-digit multiplication facts, consider having them use the cards from the first activity.

• Create a set of cards from the blackline master for each group of 2. 

• Groups of 2
• Give each group of 2 students a set of pre-cut cards.
• “Take a minute to read the directions for Compare.”
• 1 minute: quiet think time
• Play a round of Compare against the class.

• “Play Compare with your partner.”
• 10-12 minutes: partner work time

• “What were some useful strategies for comparing the expressions on the cards?” (Comparing by thinking about what the expressions mean, instead of by multiplying. For example, \(16\times6\) was greater than \(15\times6\) because it's 1 more group of 6. Breaking apart some of the large factors into smaller factors to make multiplying easier.)