Topic Two: Fluently Add and Subtract Within 10

Pacing (Duration of Unit): 10 Lessons

Desired Results

Transfer:
1. Makes 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:

  • 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.
  • 1.OA.3 Apply properties of operations as strategies to add and subtract.2 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 1.
  • 1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.
  • 1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).
  • 1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use mental strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
  • 1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.

Student "I Can" Statements:

  • I can understand how counting up is like adding and counting down is like subtracting.
  • I can subtract facts within 20.
  • I can use addition facts I know well to help me solve problems where there are more than two numbers (associative).
  • I can use what I know about addition facts to help me answer subtraction fact problems.
  • I can figure out what a missing number is in an addition or subtraction problem.
  • I can use different strategies for addition to solve word problems (within 20).

Prerequisite Standards:

  • K.OA.1Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
  • K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
  • K.OA.4 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
  • K.OA.5 Fluently add and subtract within 5.
Big Ideas:

Numbers and the Number Line
The set of real numbers is infinite and ordered. Whole numbers, integers, and fractions are real numbers. Each real number can be associated with a unique point on the number line.

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

Operation Meanings & Relationships
There are multiple interpretations of addition, subtraction, multiplication, and division of rational numbers and each operation 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 rules that govern arithmetic and algebra.

Basic Facts and Algorithms
There is more than one algorithm for each of the operations with rational numbers. Some strategies for basic facts and most algorithms for operations with rational numbers, both mental math and paper and pencil, use equivalence to transform calculations into simpler ones.

Practices, Processes, and Proficiencies
Mathematics content and practices can be applied to solve problems.
Essential Questions:

  • What strategies can you use while adding and subtracting?
Students will know...

  • You can count on to find the sum for addition facts. A number line can help you count on.
  • Doubles facts have the same number for both addends and can be used to solve problems involving real-world situations.
  • Basic addition facts that are near doubles can be found using a related doubles fact.
  • Facts with sums 6 through 10 can be broken into 5 plus some more.
  • Two numbers can be added in any order and the sum will stay the same.
  • You can count back to find the difference for subtraction facts. A number line can help you count back.
  • Addition and subtraction have an inverse relationship. This relationship can be used to solve subtraction facts; every subtraction fact has a related addition fact.
  • Drawings and equations can help you solve different types of word problems.
  • Mathematicians look for patterns in math to help solve problems.


Vocabulary:
Number line, doubles fact, near doubles fact
Students will be skilled at...

  • Adding by counting on from a number.
  • Using doubles to solve problems.
  • Solving problems using near doubles facts.
  • Using a ten-frame to solve addition facts with 5 and 10.
  • Using the same addends to write two different equations with the same sum.
  • Counting back to solve subtraction problems.
  • Using addition facts to 10 to solve subtraction problems.
  • Solve word problems by drawing pictures and writing equations.
  • using structure and identifying patterns in order to solve problems.

Assessment Evidence

Performance Assessment:
Other Evidence:

Formative Assessments:

Learning Plan

Learning Activities:

2-1 You can count on to find the sum for addition facts. A number line can help you count on.

2-2 Doubles facts have the same number for both addends and can be used to solve problems involving real-world situations.

2-3 Basic addition facts that are near doubles can be found using a related doubles fact.

2-4 Facts with sums 6 through 10 can be broken into 5 plus some more.

2-5 Two numbers can be added in any order and the sum will stay the same.

2-6 You can count back to find the difference for subtraction facts. A number line can help you count back.

2-7 Addition and subtraction have an inverse relationship. This relationship can be used to solve subtraction facts; every subtraction fact has a related addition fact.

2-8 Addition and subtraction have an inverse relationship. This relationship can be used to solve subtraction facts; every subtraction fact has a related addition fact.

2-9 Drawings and equations can help you solve different types of word problems.

2-10 Good math thinkers look for patterns in math to help solve problems.
Resources:

Problem of the Month:


Centers:



SmartBoard Resources/Games:

*