Partial products algorithm with numbers to 100

General

Students lean to calculate partial products with a number to 100.

Standards

CCSS.Math.Content.4.NBT.B.5

Learning objective

Students will be able to calculate partial products, with a number less than 10 and a number to 100.

Introduction

State a problem, for which a number is multiplied by a tens number. Next you throw a ball and the student that catches the ball must give the answer to the problem. If the student gives the correct answer, then they throw the ball back and you repeat these several times.

Instruction

Explain that with partial products you put the numbers of the problem one under the other. Next you can multiply them together by working from left to right. Explain that you put the largest number of the problem on top and the other number underneath. With partial products multiplication you calculate from left to right. So you start by multiplying the tens numbers. Then you multiply the ones number. You put these answers in the chart and state what the intermediate problems are. If you add up the numbers from the chart, you know what the answer is. You put this answer at the bottom of the chart. Next there is a problem in a chart, for which each time there is a different row marked in yellow. Ask the students if they know which intermediate problem belongs in each colored row. This is how you can check if students know which steps they must go through. Then you show a chart, for which the intermediate steps must be filled in. Have the students write these numbers down and hold them up so you can check their work. Then practice partial products with two more problems, one of which has the chart already filled in and the other must still be filled in.

Check whether the students can multiply partial products by asking the following questions:
- Why is it useful to be able to multiply using partial products?
- What do the letters H T O mean?
- Where do you always start when calculating partial products?
- Solve this problem using partial products: 27 × 9

Quiz

The students test their understanding of partial products with numbers to 100 through ten exercises. For some questions the students must determine the intermediate steps in calculating the product. For the other exercises the students must solve the problem. Some HTO charts have been filled in already, and some the students must fill in on their own.

Closing

You discuss with the students once again that it is important to be able to multiply partial products with a number to 100, because that is how you can solve problems in simple steps. Check whether the students know that they calculate partial products by working from left to right. Have the students solve two more problems using partial products. Ask the students how they filled in the chart.

Teaching tips

When students have difficulty with multiplying using partial products, you can repeat the meaning of H T O and how you fill in the numbers of a problem in the HTO chart. Write out the intermediate problems. You may also label the tens number and the ones values, so that it is obvious what is being multiplied together.