Interactive base ten blocks for decimals2/13/2024 ![]() Another main idea is bundling: we can group 10 of any base-ten unit into 1 of a base-ten unit that is 10 times as large. One main idea in this lesson is that addition of decimals beyond hundredths works the same way as addition of whole numbers and decimals up to hundredths: all of them rely on combining the values of like base-ten units. If the numbers contain more decimal places or larger digits, the diagrams would take a lot of time to draw.) Which is more efficient, using base-ten blocks or calculating the difference? (For some numbers, such as \(1.26 - 0.14\), both methods are efficient.Why is it helpful to line up the decimal points when calculating differences of decimals? (Aligning the points helps us align digits with the same place value.).Did anyone find different results when using diagrams versus when calculating vertically? If so, where did the error happen and what might have caused it?. ![]() How are addition and subtraction of decimal numbers similar? (It is important to attend to place value and to add or subtract numbers that represent the same base-ten units.).Highlight how the different sizes of the base-ten units in the diagram informs how we subtract one decimal from another. Then, discuss: Select a few students to share their responses and reasonings for the last two questions. The goal of the whole-class discussion is to make sure students understand that when we perform subtraction without diagrams, it is essential to pay close attention to place value in the numbers. The algorithm works well in all cases, but it is more abstract and requires that all bundling be recorded in the right places.) The drawings become hard when there are lots of digits or when the digits are large. ![]() “Which method of calculating is more efficient?” (It depends on the complexity and size of the numbers.“How can the bundling process be represented in vertical calculations?” (We can show that the 8 hundredths and 9 hundredths make 1 tenth and 7 hundredths by recording 7 hundredths and writing a 1 above the 3 tenths in 0.38.).This 1 tenth is added to the 3 tenths and 6 tenths, which makes 10 tenths. “In which place(s) did bundling happen when adding 0.38 and 0.69?” (In the hundredth and tenth places.) “Why?” (There is a total of 17 hundredths, and 10 hundredths can be bundled to make 1 tenth.Highlight how drawings can effectively help us understand what is happening when we add base-ten numbers before moving on to a more generalized method. Discuss: The larger square represents 1.įocus the whole-class debriefing on the idea of choosing appropriate tools to solve a problem, which is an important part of doing mathematics (MP5). Check your calculation against your diagram in the previous question.įind each sum. Can you find the sum without bundling? Would it be useful to bundle some pieces? Explain your reasoning. Find the value of \(0.38 + 0.69\) by drawing a diagram.How this “bundling” is represented in the vertical calculation. ![]()
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