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Multiply by 1,000
Students will be able to multiply by multiples of 10, up to 1,000.
- Have students count by 10 aloud.
- Explain, "Each of the numbers we counted is a multiple of ten."
- Ask, "What is 3 tens? 5 tens? 10 tens?"
- Tell students that today we will be multiplying numbers by multiples of ten.
Explicit Instruction/Teacher modeling(10 minutes)
- On the board, write 4 x 1 = 4, 4 x 10 = 40, 4 x 100 = 400, and *4 x 1,000 = 4,000.
- Point at each equation and read the products aloud as ‘four ones,’ ‘four tens,’ ‘four hundreds,’ ‘four thousands.’
- Point out that, when multiplied by ten, the four is in the tens place and its value is ten times what it was in the ones place. When four is multiplied by 100, it’s value is ten times what it was in the previous equation.
- Ask students to look at the problems on the board and talk to a partner about any patterns they notice. Call on students to share their observations (i.e. each product has one more zero than the previous product; each product has the same number of zeros as there are in the equation).
- Write a second example on the board: 40 x 1 = 40, 40 x 10 = 400, 40 x 100 = 4,000, and 40 x 1,000 = 40,000.
- Read each product aloud as ‘forty ones,’ ‘forty tens,’ ‘forty hundreds,’ and ‘forty thousands.’
- Ask students to look for patterns in the new example and discuss as a class.
- Explain, "In this example, we also notice that each product is ten times more than last. For instance, 400 is ten times more than 40."
- Tell students that a digit in one place represents ten times what it represents in the place to its right. And, each time the value of a number increases by ten, a zero added due to the additional place value.
- Explain, "When we are multiplying with multiples of ten, a shortcut we can use is to add zeros. The number of zeros in the equation will match the number of zeros in the product (underline zeros in the example on the board 40 x 10 = 400)."
- Write a problem on the board, like 60 x 100.
- Demonstrate the shortcut by underlining the basic fact (6 x 1). Then, count the zeros (three zeros). Explain, that since we know that 6x1 is six, we can write six and then add three zeros to find the answer (6,000).
Guided Practice(15 minutes)
- Write a problem on the board, like 80 x 100, and have students solve it with a partner.
- Model an example with one factor that is not a multiple of ten (i.e. 25 x 1 = 25, 25 x 10 = 250, 25 x 100 = 2500, and 25 x 1,000 = 25,000).
- Write a problem on the board, like 74 x 1,000. Have students solve it with a partner.
- Model an example in which neither multiple of ten contains a one (i.e. 5 x 3 = 15, 5 x 30 = 150, 50 x 30 = 1,500, and 50 x 300 = 15,000).
- Remind students they can use the basic fact (5 x 3) and then count zeros to find the product.
- Write a problem on the board, like 60 x 40. Have students solve it with a partner.
Independent working time(15 minutes)
- Hand out the Multiply by 1,000 worksheet and go over the example with the class.
- Complete the first problem with the class, then instruct students to complete the worksheet independently.
- Circulate as students work and offer support as needed.
- Go over the worksheet as a class.
- Provide partially completed worksheets or examples to students so that they can see parts of the pattern and fill in missing numbers.
- Provide additional practice with smaller numbers, like 30 x 6 (see resources for a worksheet).
- Have students continue the pattern with larger numbers (i.e. 200 x 70,000).
- Roll two dice and use the numbers to write four multiplication equations (i.e. if you rolled two and four, you might write 2 x 4 = 8, 20 x 4 = 80, 20 x 40=800, 20 x 400 = 8,000).
- Pass out dice to students and instruct them to roll the dice and use the numbers they’ve rolled to write their own four equations.
- Collect and check for understanding.
Review and closing(5 minutes)
- Ask students, "How can this strategy (multiplying by multiples of 10) help us understand and solve bigger multiplication problems?"
- Discuss as a class (i.e. we can solve big problems in our head; we know that a digit in one place represents ten times what it represents in the place to its right).