The math learning center is an app and online platform that allows …
The math learning center is an app and online platform that allows students to use manipulatives virtually. In this activity, students will use virtual manipulatives to add fractions with unlike denominators
This short video and interactive assessment activity is designed to teach fifth …
This short video and interactive assessment activity is designed to teach fifth graders about adding, subtracting, multiplying, and dividing with parentheses.
Unit 5: Arithmetic in Base Ten Lesson 3: Adding and Subtracting Decimals …
Unit 5: Arithmetic in Base Ten Lesson 3: Adding and Subtracting Decimals with Few Non-Zero Digits
As with addition, prior to grade 6 students have used various ways to subtract decimals to hundredths. Base-ten diagrams and vertical calculations are likewise used for subtracting decimals. “Unbundling,” which students have previously used to subtract whole numbers, is a key idea here. They recall that a base-ten unit can be expressed as another unit that is 1/10 its size. For example, 1 tenth can be “unbundled” into 10 hundredths or into 100 thousandths. Students use this idea to subtract a larger digit from a smaller digit when both digits are in the same base-ten place, e.g., 0.012 - 0.007. Rather than thinking of subtracting 7 thousandths from 1 hundredth and 2 thousandths, we can view the 1 hundredth as 10 thousandths and subtract 7 thousandths from 12 thousandths.
Unbundling also suggests that we can write a decimal in several equivalent ways. Because 0.4 can be viewed as 4 tenths, 40 hundredths, 400 thousandths, or 4,000 ten-thousandths, it can also be written as 0.40, 0.400, 0.4000, and so on; the additional zeros at the end of the decimal do not change its value. They use this idea to subtract a number with more decimal places from one with fewer decimal places (e.g., 2.5 - 1.028). These calculations depend on making use of the structure of base-ten numbers (MP7).
The second activity is optional; it gives students additional opportunities to practice summing decimals.
Unit 5: Arithmetic in Base Ten Lesson 4: Adding and Subtracting Decimals …
Unit 5: Arithmetic in Base Ten Lesson 4: Adding and Subtracting Decimals with Many Non-Zero Digits
This lesson strengthens students’ ability to add and subtract decimals, enabling them to work toward fluency. Students encounter longer decimals (beyond thousandths), find missing addends, and work with decimals in the context of situations. They decide which operation (addition or subtraction) to perform and which strategy to use when finding sums and differences. They also reinforce the idea that we can express a decimal in different but equivalent ways, and that writing additional zeros after the last non-zero digit in a decimal does not change its value. Students use this understanding to practice subtracting numbers with more decimal places from those with fewer decimal places (e.g., 1.9 - 0.4563).
To solve these problems, students must lean heavily on their understanding of base-ten numbers (MP7). Given problems such as 7 - ? = 3.4567 and 0.404 + ? = 1, they need to think carefully about the meaning of each place value, the meaning of addition and subtraction, and potential paths toward the solution. Along the way, they also begin to see patterns in the calculations, which enables them to become increasingly fluent in finding sums and differences (MP8).
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