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.
Use a standard algorithm to add, subtract, multiply, and divide multi-digit decimals.
Algorithms are reliable procedures for finding results. Steps can be forgotten. Understanding, however, is not forgotten. Students should be able to explain how standard algorithms work.
Estimate a sum, difference, product, or quotient to determine if a result is reasonable.
Determining the reasonableness of one's solution is critical in learning mathematics and applying it to everyday life. This is also true when working with algorithms. Estimating results helps students determine if the procedures they applied were accurate. Estimating itself should be a procedure. Instead, students should make use of friendly, compatible numbers to estimate results. Students should consistently estimate their solutions first, find solutions with algorithms, and then compare results with the estimates.
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).
Algorithms are reliable but not always efficient. Efficiency is grounded in one's understanding of numbers, number relationships, operations, and so on. Fluent students don't blindly use algorithms. Instead, they determine when algorithms would be useful or efficient and when they are not.
Essential vocabulary for this standard includes: 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).
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. The resources below can be used to measure student understanding of the standard. This rubric can be applied to tasks and observations for assessment and/or grading.