In this Warm-up, students review multiplication of decimals and estimate the size of a product given the size of the decimal factors. They explain why their estimates are reasonable based on their understanding of place value and multiplication.
To make reasonable estimates, students need to look for and make use of structure (MP7). In explaining why their choice is the best estimate, students need to be precise in their word choice and use of language (MP6).
Tell students to close their books or devices (or to keep them closed). Explain that they will see four multiplication expressions, displayed one at a time. For each expression, there will be three possible estimates of its value. Their job is to select the best estimate and to be able to explain why it is the best.
Reveal one expression at a time. For each expression:
For each multiplication expression, choose the best estimate of its value. Be prepared to explain your reasoning.
(6.8)⋅(2.3)
74⋅(8.1)
166⋅(0.09)
(3.4)⋅(1.9)
Focus the discussion on how the given factors can inform our estimate of each product. Emphasize that even if we were to calculate the products precisely, we can use estimation and our understanding of place value to check if our answers make sense.
Students who know how to perform multiplication computation and use a “count the number of decimal places'' strategy might mix that method with estimation in placing the decimal point. For example, to estimate 74⋅(8.1), they might round the factors to 70 and 8 and find a product of 560. Seeing that there is a total of 1 place after the decimal point in the original factors, they place the decimal point to the left of the last digit and choose 56 as their answer. Prompt students to think about the reasonableness of their answer relative to the factors (for instance, ask if 56 is a reasonable product of 70 and 8).
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In this Warm-up, students review multiplication of decimals and estimate the size of a product given the size of the decimal factors. They explain why their estimates are reasonable based on their understanding of place value and multiplication.
To make reasonable estimates, students need to look for and make use of structure (MP7). In explaining why their choice is the best estimate, students need to be precise in their word choice and use of language (MP6).
Tell students to close their books or devices (or to keep them closed). Explain that they will see four multiplication expressions, displayed one at a time. For each expression, there will be three possible estimates of its value. Their job is to select the best estimate and to be able to explain why it is the best.
Reveal one expression at a time. For each expression:
For each multiplication expression, choose the best estimate of its value. Be prepared to explain your reasoning.
(6.8)⋅(2.3)
74⋅(8.1)
166⋅(0.09)
(3.4)⋅(1.9)
Focus the discussion on how the given factors can inform our estimate of each product. Emphasize that even if we were to calculate the products precisely, we can use estimation and our understanding of place value to check if our answers make sense.
Students who know how to perform multiplication computation and use a “count the number of decimal places'' strategy might mix that method with estimation in placing the decimal point. For example, to estimate 74⋅(8.1), they might round the factors to 70 and 8 and find a product of 560. Seeing that there is a total of 1 place after the decimal point in the original factors, they place the decimal point to the left of the last digit and choose 56 as their answer. Prompt students to think about the reasonableness of their answer relative to the factors (for instance, ask if 56 is a reasonable product of 70 and 8).