Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Learning Targets (I can)
Explain how standard algorithms for addition, subtraction, multiplication, and division with decimals work.
Estimate a sum, difference, product, or quotient to determine if a result is reasonable.
Use a standard algorithm to add, subtract, multiply, and divide multi-digit decimals.
Determine if the standard algorithm is necessary and/or efficient (i.e. 14.518 - 3.5 can be solved with an algorithm but it is less efficient than using mental mathematics).
About the Math
Explain how standard algorithms for addition, subtraction, multiplication, and division with decimals work.
Procedural fluency is defined by the Common Core as "skill in carrying out procedures flexibly, accurately, efficiently and appropriately." In 4th and 5th grades, students added and subtracted decimals. Multiplication and division of decimals were introduced in 5th grade (decimals to the hundredths place). At the elementary level, these operations were based on concrete models or drawings and strategies based on place value, properties of operations, and/or relationship between addition and subtraction. Understanding of algorithms is grounded in the understanding of these concepts.
Estimate a sum, difference, product, or quotient to determine if a result is reasonable.
Students should estimate their results before calculating. They should compare their results to their estimated predictions. Students should discuss and share strategies. Estimation should extend beyond rounding. Students should also find ranges and estimates with friendly or compatible numbers. Students should be able to reason about the result. For example, 239.98 + 112.01 will be about 350 (estimating with the wholes) or about 352 (estimating 239 to be 240 and adding 112).
Use a standard algorithm to add, subtract, multiply, and divide multi-digit decimals.
The standard algorithm for all of these operations must be grounded in understanding. It is not simply "line up the decimal points" or "count the place values and move the decimal to the right or left." These "rules" are forgotten without understanding. Students should make connections between algorithms with whole numbers and algorithms with decimals. Students should continue to estimate results to confirm reasonableness.
Determine if the standard algorithm is necessary and/or efficient (i.e. 14.518 - 3.5 can be solved with an algorithm but it is less efficient than using mental mathematics).
Knowing how to do an algorithm must be complemented by when to do an algorithm. These conversations should happen consistently so that students begin to determine when algorithms are useful and when they are inefficient. Additionally, students should consider when a tool like a calculator will be more efficient than an algorithm.
Essential vocabulary for this standard includes algorithm, sum, quotient, product, factor, addend, minuend, difference, divisor, dividend, tenths, hundredths, and whole number.
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Explain how standard algorithms for addition, subtraction, multiplication, and division with decimals work.
Estimate a sum, difference, product, or quotient to determine if a result is reasonable.
Use a standard algorithm to add, subtract, multiply, and divide multi-digit decimals.
Determine if the standard algorithm is necessary and/or efficient (i.e. 14.518 - 3.5 can be solved with an algorithm but it is less efficient than using mental mathematics).
Reinforce through work with 6.EE standards.
Reinforce through work with 6.G and 6.RP standards.
Explain how standard algorithms for addition, subtraction, multiplication, and division with decimals work.
Estimate a sum, difference, product, or quotient to determine if a result is reasonable.
Use a standard algorithm to add, subtract, multiply, and divide multi-digit decimals.
Determine if the standard algorithm is necessary and/or efficient (i.e. 14.518 - 3.5 can be solved with an algorithm but it is less efficient than using mental mathematics).
These tasks can be used with small group or whole group instruction.
You divide two numbers and the answer is 2.5. What two numbers might you have divided? Write a story problem for your equation.
How is adding and subtracting with decimals similar to adding and subtracting with whole numbers? How are they different?
Why do you “line up the decimal points” when you are adding and subtracting with decimals? Why does that make sense mathematically?
What role does estimating play when you multiply and divide with decimals? Use examples to support your answer.
Can you create an addition, a subtraction, a multiplication, and a division equation where the answer is 95.4?
Solve both 15 x 28 and 1.5 x 28. What is alike and what is different? Why do you “count the decimal points”?
Use estimation to place the decimal point in the answer.
8.432 x 5.75 = 48484
306.15 ÷ 75.4 = 40603448
3.044 x 16.5 = 50226
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
6-8
Calculator Decimal Counting, Activity 9.1, Page 144 Represent and Review, Activity 9.11, Page 157 Where Does the Decimal Go? Multiplication, Activity 9.12, Page 160 Where Does the Decimal Go? Division, Activity 9.13, Page 162
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
Explain how standard algorithms for addition, subtraction, multiplication, and division with decimals work.
Estimate a sum, difference, product, or quotient to determine if a result is reasonable.
Use a standard algorithm to add, subtract, multiply, and divide multi-digit decimals.
Determine if the standard algorithm is necessary and/or efficient (i.e. 14.518 - 3.5 can be solved with an algorithm but it is less efficient than using mental mathematics).
Learning targets identify what students should be able to do. This rubric can be applied to tasks and observations for assessment and/or grading.