Snap Cubes Use Two Different Colors to Build Related Fact Trains
Global Concept Guides: Related Facts, Operations and Equations, and Ways to Make 20
Prior Learning: K.OA.1, K.OA.2, K.OA.3, K.OA.4, K.OA.5
Progressions Document Link
Show What You Know Task:Use the Go Math Chapter 5 Show What You Know (p. 182 and 183)
Common Core State Standards for Mathematical Content:
Represent and solve problems involving addition and subtraction.
1.OA.1Use addition and subtraction within (10) 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
Add and subtract within 20.
1.OA.6Add and subtract within (10) 20, demonstrating fluency for addition and subtraction within 10. Use 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).
Work with addition and subtraction equations.
1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
1.OA.8Determine 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 = . / Comments:
This is a critical area for first grade students. Building strategies over time is crucial to building fluency within 20 by the end of the year. Beginning with concrete and connecting to equations bridge student understanding.
Notes on Assessment:
Use Chapter 5 Go Math Assessment
See Common Performance Task link below
Unpacking the Standards for this Unit:
According to Adding it Up, “Traditional representational activities of algebra center on the formation of algebraic expressions and equations. Creating these expressions and equations involves understanding the mathematical operations and relations and representing them through the use of letters and-for equations-the equal sign. It also requires thinking that proceeds in rather different ways from the thinking that develops in traditional arithmetic. In the transition from arithmetic to algebra, students need to make many adjustments, even those students who are quite proficient in arithmetic. At present, for example, elementary school arithmetic tends to be heavily answer oriented and does not focus on the representation of relations (p. 261)”
Common Performance Task with Rubric for this Unit:
Students will use number cards to determine related facts, determine true/false equations, and identify strategies used to solve for an unknown.
Click herefor Performance Task and Rubric.
Future learning:
Students can continue to represent any situation with a situation equation and connect such equations to diagrams. Such connection can help students to solve the more difficult problem situation subtypes by understanding where the totals and addends are in the equation and rewriting the equation as needed (Progressions for the Common Core State Standards in Mathematics, 2012, p. 17).
1st / Global Concept 1 of 3 for this Unit of Study: Related Facts
Using related facts to solve addition and subtraction strategies / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can you determine which facts are related?
Day 2: How do related facts help you find the missing number?
Day 3: How can you use the relationship between addition and subtraction to help you solve problems?
Related Go Math Chapter Test Questions: Unit 6 Go Math Ch. 5 Test # 3 – 8, 11 - 12
Instructional Resources
Manipulatives:
- Snap Cubes –use two different colors to build related fact ‘trains’
- Student number lines—match up with snap cube train
- Triangle Flash Cards—Mountain Cards found in Go Math Manipulative Kit
- Dominoes
- Two-Sided Counters
- Go Math Lesson 5.2 (Listen and Draw) - 5.3 (Model and Draw, HOT Question)
- Voyages Excursion Lesson All Aboard TE 89-91—Use number cards to manipulate the numbers to create an equation.
- Go Math Lesson 5.5 - 5.6 (Problem Solving)
- Illuminations Do It With Dominoes Lesson 6 Finding Fact Families
- iTools Counters
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1,3)
- How do you know if addition and subtraction facts are related?
- How did you know which number was the sum?
- How do related facts help you find missing numbers?
- How does knowing one fact family sentence help you write the other sentences?
- Using the same numbers, write more than one equation that is true.
Our students are able to…
- Make a model to show the related facts (SMP 4).
- Find pattern and structure in related facts (SMP 7).
- Notice that knowing one number sentences can be a shortcut to knowing other number sentences that make that fact family (SMP 8).
- Construct arguments using concrete referents such as objects, drawing, models, and number sentences (SMP 3).
- Provide opportunities to explore related facts with multiple hands on tools (SMP 4).
- Scaffold questioning and discussion to highlight the structure of related facts (SMP 7).
- Connect learning of related facts as a shortcut to solving for missing numbers (SMP 8).
- Probe students to be explicit in their explanations and nurture an environment that supports discussion; both justifying and critiquing (SMP 3).
1st / Global Concept 2 of 3 for this Unit of Study: Operations and Equations
Understand the meaning of the equal sign and determine if the equations are true or false / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can making a model help you solve a problem?
Day 2: What are the meanings of equal to or not equal to?
Day 3: How can you decide if a number sentence is true or false?
Related Go Math Chapter Test Questions: Unit 6 Go Math Ch. 5 Test # 1 – 2, 9 - 10, 13 - 15
Instructional Resources
Manipulatives:
- Snap Cubes –use two different colors to build bar models
- Two-colored Counters—Model problem situations
- Pan Balance—to demonstrate “equal to” or “same as”
- Operation Cards—use to help students orally read the number sentences correctly.
- Go Math Lesson 5.1, pp. 185 – 188 use bar model to connect to operation of add and subtract.
- Voyages Excursion Lesson, Balance Me, TE p. 81 – 84
- Go Math Lesson 5.9, pp. 217-220
- iTools -Primary Algebra Number Balance
- DreamBox Learning Math Lesson Equivalency 0 to 20
- Mega Math Country Countdown, Counting Critters, Level T, Level M, Level H
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1,3)
- Did everyone’s model show the same value? Do the models appear the same?
- How does a bar model change when using different numbers?
- How do you choose when to add or subtract?
- How can different number sentences have the same sum or difference?
Our students are able to…
- Construct viable arguments and critique the reasoning of others (SMP 3).
- Build equations to represent a problem (SMP 2).
- Using strategies to determine if equations are true or false (SMP 2).
- Understanding the various strategies used by others when solving problems (SMP 1).
- Facilitate discussion among students to use precise language in arguing and critiquing (SMP 3 and 6).
- Provide opportunities for students to read and listen to problems and explore building equations and models (SMP 1 and 4).
- Design opportunities for students to decontextualize problems by modeling ways that operations and equations symbolize situations (SMP 2).
1st / Global Concept 3 of 3 for this Unit of Study: Ways to Make 20
Use addition and subtraction strategies to find different ways to make 20, and relate subtraction to addition. / Projected Time Allotment:
2 days
Sample Essential Questions:
Day 1: How can you add and subtract in different ways to make the same number?
Day 2: How can addition and subtraction strategies help you find sums and differences?
Related Go Math Chapter Test Questions: Unit 6 Go Math Ch. 5 Test #18-24
Instructional Resources
Manipulatives:
- Two-colored Counters—Model problem situations
- Snap Cubes –use three different colors to model different sums or differences
- Dominoes/Dot Cards Teacher Resources BLM 19 -20—children work in pairs to write related addition facts to build fluency within 20.
- Go Math 5.8: pp. 213 - 216
- Go Math 5.10: pp. 221 – 224 (model the strategy of Lesson 5.4 pp. 198-199 to help build fluency and check accuracy by using addition to check subtraction).
- Primary iTools—Snap Cubes
- DreamBox Learning Math Lesson Equivalency 0 to 20
- FASTT Math-settings Addition 0-9
- Mega Math,Country Countdown, Counting Critters, Level U
Sample HOT Questions: Use these to facilitate student discussion. (SMP 1,3)
- How can you show the sum of a number in more than one way?
- Judy says it is possible to make a number with more than two addends. Do you agree or disagree with her thinking? Explain.
- Why would using addition to check subtraction be a useful strategy?
- When can you use the strategy of check subtraction using addition?
- How can knowing related facts help you build fluency?
- Why might someone have a different way to make 20 than you?
Our students are able to…
- Construct viable arguments and critique the reasoning of others (SMP 3).
- Analyze mathematical relationships to draw conclusions (SMP 4).
- Add and subtract within 20 with precision (SMP 6).
- Facilitate discussion among students to use precise language in arguing and critiquing (SMP 3 and 6).
- Provide opportunities for students to read and listen to problems and explore building equations and models (SMP 1 and 4).