Topic Two: Adding and Subtracting Decimals

Desired Results

Transfer:
1. Makes sense of problems and perseve
re in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Established Goals:
  • 5.NBT.4: Use place value understanding to round decimals to any place.
  • 5.NBT.7: Perform operations with multi-digit whole numbers and decimals to hundreths. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Student "I Can" Statements"
  • I can use place value understanding to round decimals to any place.
  • I can add, subtract, multiply, and divide decimals to hundreths. I can use concrete models or drawings to explain the method used.

Pre-Requisite Standards:
  • 4.NF.6:Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100 ; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
  • 4.NF.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
  • 5.NBT.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
Big Ideas:
  • Basic Facts and Algorithms: There is more than one algorithm for each of the operations with rational numbers. Most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform the calculations into simpler ones.
  • Numbers and the Number Line: The set of numbers is infinite and ordered. Whole numbers and decimals are real numbers Each real number can be associated with a unique point on the number line.
  • Estimation: Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute with mentally.
  • Patterns, Relations, and Functions: Relationships can be described and generalizations made for mathematical situations that have numbers or objects that repeat in predictable ways.
  • Practices, Processes, and Proficiencies: Mathematics content and practices can be applied to solve problems.
Essential Questions:
  • How can sums and differences of decimals be estimated?
  • What are the standard procedures for adding and subtracting whole numbers and decimals?
Students will know...
  • There is more than one way to do a mental calculation. Techniques for doing addition or subtraction calculations mentally invovlveve changing the numbers so the calculation is easy to do mentally.
  • Models and algorithms for adding or subtracting mult-digit decimals are just an extension of models and algorithms for adding or subtracting multi-digit whole numbers.
  • Adding or subtracting multi-digit decimals is similar to adding or subtracting whole-digit whole numbers.
  • A number line can be used to round whole numbers and decimals by making it easy to see which multiple of 10, 100, etc. or of 0.1, 0.01, etc. a number is closets to.
  • There is more than one way to estimate a sum or difference. Each estimation technique gives one way to estimate by replacing numbers with other numbers that are close and easy to compute with mentally.
  • Some sequence of numbers or objects repeat or grow in predictable ways.
  • Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation.
  • Some problems can be solved by first finding and solving a sub-problem(s) and then be using that answer(s) to solve the original problem.

Vocabulary: Commutative Property, Associative Property, compensation, compatible numbers, rounding

Students will be skilled at...
  • Computing sums and differences mentally using the Commutative and Associative Properties of Addition, compatible numbers, and compensation.
  • Rounding whole numbers through millions and decimals through thousandths.
  • Using rounding and compatible numbers to estimate sums and differences fo whole numbers and decimals.
  • Adding and subtracting decimals in tenths and hundreths using models.
  • Using pictures and writing equations to help them solve problems.
  • Computing sums of decimals involving tenths, hundreths, and thousanths.
  • Computing differences of decimals involving tenths, hundreths, and thousanths.
  • Using multiples steps to solve a variety of problems.

Assessment Evidence

Performance Assessment Task:
Fractions-5.NBT.3
Formative Assessment:

Learning Plan

Learning Activities:
2-1: There is more than oen way to do mental calculations involving decimals. Most techniques involving changing one or more numbers (or the arrangement of numbers) so the calcualtion that results is easy to do mentally.
2-2: A number line can be used to round whole numbers and decimals by making it easy to see which multiple of 10, 100, etc. or of 0.1, 0.01, etc. a number is closets to.
2-3: There is more than one way to estimate a sum or difference. Each estimation technique gives one way to estimate by replacing numbers with other numbers that are close and easy to compute with mentally. Some sequence of numbers or objects repeat or grow in predictable ways.
2-4: Models and algorithms for adding or subtracting mult-digit decimals are just an extension of models and algorithms for adding or subtracting multi-digit whole numbers.
2-5: Information in a problem can often be shown using a diagram and used to solve the problem. Some problems can be solved by writing and completing a number sentence or equation.
2-6: Adding or subtracting multi-digit decimals is similar to adding or subtracting whole-digit whole numbers.
2-7: Adding or subtracting multi-digit decimals is similar to adding or subtracting whole-digit whole numbers.
2-8: Some problems can be solved by first finding and solving a sub-problem(s) and then be using that answer(s) to solve the original problem.
Resources:

Home-School Connection:


Problem of the Month:
Diminishing Return-5.NBT.7
Get Your Number-5.NBT.7

Centers:
Rounding Decimals to the Nearest Hundreth-5.NBT.4
Decimals of the Week-5.NBT.7
Base Ten Pictures with Decimals-5.NBT.7
Base Ten Buildings with Decimals-5.NBT.7
Base Ten Decimal Bag Addition-5.NBT.7
Base Ten Decimal Bag Subtraction-5.NBT.7
Total Ten-5.NBT.7
Decimal Cross Number Puzzles-5.NBT.7
Decimal Subtraction Spin-5.NBT.7
Decimal Addition to 500-5.NBT.7
Decimal Addition Bingo-5.NBT.7
Decimal Race to Zero-5.NBT.7
Decimal Magic Triangle-5.NBT.7
Magic Squares-5.NBT.7

SmartBoard Activities:
Estimate (Whole Numbers and Decimals)