The purpose of this activity is for students to see how, when multiplying a number greater than 10, the distributive property can be used to decompose the factor into tens and ones, creating two smaller products. Base-ten blocks and base-ten diagrams are used to help students visualize what is happening when a factor is decomposed to make two easily known products. Factors that are teen numbers can be naturally decomposed into a ten and some ones using place value. This will be useful in subsequent lessons as students progress towards fluent multiplication and division within 100.

When students see that you can decompose a teen number into tens and ones and use this to multiply teen numbers, they look for and make use of structure (MP7).

• Display base-ten blocks or base-ten diagrams that students used to solve. As students explain their work, write multiplication expressions to represent them.
• “How does this diagram (or the base-ten blocks) show how Tyler’s method could be used to multiply ?” (We can see there are 3 tens which is 30. We can see that there are 3 groups of 4 ones which is 12. is 42. The whole diagram represents , so the product is 42.)
• If there is time, ask students to find the value of and using the base-ten blocks and Tyler’s strategy.

The purpose of this activity is for students to make sense of different ways of representing multiplication of a teen number. Students analyze a gridded area diagram, base-ten blocks, and an area diagram labeled with side lengths. When they discuss how the different diagrams represent the same product, students reason abstractly and quantitatively (MP2).

• “How are these ways of representing the same?” (They all show the 15 being decomposed into 10 and 5. They are all shaped like a rectangle.)
• “How are these ways of representing different?” (Clare used base-ten blocks, but Andre and Diego used rectangles. Diego didn’t show the squares in his rectangle, but Clare and Andre did.)
• “How could we represent the strategy shown in all the diagrams with expressions?” ( and or and .)