Topic Two: Number Sense: Addition and Subtraction

Desired Results

Transfer: Standards for Mathematical Practices

1. Make sense of problems and persevere 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:
3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Student I Can Statements:
  • I can add within 1000 by using an algorithm or strategy based on place value.
  • I can subtract within a 1000 by using an algorithm or strategy based on place value.

Prerequisite Standards:
2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations.

2.NBT.7 Add and subtract within 1000, 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. Understand that in addition or subtracting three-digit numbers, one adds or subtracts hundred and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens and hundreds.

2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations.
Big Ideas:
Operation Meanings and Relationships
There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers, and each operations is related to other operations.

Properties
For a given set of numbers there are relationships that are always true called properties, and these are the rule that govern arithmetic and algebra.

Algorithms
There is more that 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 calculations into simpler ones.

Estimation
Numbers can be approximated by numbers that are close. Numerical calculations can be approximated by placing numbers with other numbers that are close and easy to computer with mentally.

Equivalence
Any number, measure, numerical expression, algebraic expression, or equation can be represented in an infinite number of ways that have the same value.

Practice, Processes, and Proficiencies
Mathematics content and practices can be applied to solve problems.
Essential Questions:
  • How can sums and differences be found mentally?

  • How can sums and differences be estimated?
Students will know...
  • Two numbers can be added in any order, the sum of any number and 0 is that number; and three or more numbers can be grouped and added in any order.
  • Some real-world problems involving joining, separating, part-part-whole, or comparison can be solved using addition or subtraction.
  • There is more than one way to do a mental calculation. Techniques for doing addition or subtraction calculations mentally involve changing the numbers or the expressions so the calculation is easy to do mentally.
  • Different numerical expressions can have the same value. Or, the value of one expression can be less than (or greater than) the value of the other expression.
  • Rounding is a process of finding the multiple of 10, 100, etc. closet to a given number.
  • There is more than one way to estimate a sum or difference. Rounding and substituting compatible numbers are two ways to estimate sums and differences.
  • An equation shows a balance between what is on the right side and what is on the left side of the equal sign.
  • Answer to problems should always be checked for reasonableness, and this can be done in different ways. Two ways are to use estimation when appropriate and to check the answer against the question and conditions in the problem.

Vocabulary:
  • addends
  • sum
  • commutative (order) property of addition
  • Associative property of addition
  • Identity property of addition
  • difference
  • fact family
  • round
  • estimate
  • compatible numbers
  • equation


Students will be able to...
  • Use concrete materials and concepts of addition to model the Commutative, Associative, and Identity Properties of Addition.
  • Recognize situations when subtraction is used to so problem and write number sentences.
  • Solve problems by adding with mental math.

Assessment Evidence

Performance Tasks:



Writing Task

Other Evidence:

Formative Assessments:





Learning Plan

Learning Activities:

2-1 Two numbers can be added in any order, the sum of any number and 0 is that number; and three or more numbers can be grouped and added in any order.

2-1, 2-2 Some real-world problems involving joining, separating, part-part-whole, or comparison can be solved using addition or subtraction.

2-3, 2-4 There is more than one way to do a mental calculation. Techniques for doing addition or subtraction calculations mentally involve changing the numbers or the expressions so the calculation is easy to do mentally.

2-5 Different numerical expressions can have the same value. Or, the value of one expression can be less than (or greater than) the value of the other expression.

2-6 There is more than one way to estimate a sum or difference. Rounding and substituting compatible numbers are two ways to estimate sums and differences.

2-7 There is more than one way to estimate a sum or difference. Rounding and substituting compatible numbers are two ways to estimate sums and differences.

2-8 An equation shows a balance between what is on the right side and what is on the left side of the equal sign.

2-9 Answer to problems should always be checked for reasonableness, and this can be done in different ways. Two ways are to use estimation when appropriate and to check the answer against the question and conditions in the problem.
Resources:

Home School Connection:


Centers:





Online Games:
Sum Cloud Challenge

Homework:



Online Student Videos:
Learn Zillion Online Student Videos
CyberChase PBS Bianca on the Run

Online Teacher Videos:
Mental Math Third Grade
Talking About Math: Sharing Strategies