Global Concept Guides: Related Facts, Operations and Equations, and Ways to Make Numbers within 20
Prior Learning: MAFS.K.OA.1.1, MAFS.K.OA.1.2,MAFS.K.OA.1.4, MAFS.K.OA.1.5
Progressions Document Link
Show What You Know Task: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.
MAFS.1.OA.1.1 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]Students are not required to independently read the word problems.)
Add and subtract within 20.
MAFS.1.OA.3.6Add and subtract within 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.
MAFS.1.OA.4.7 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.
MAFS.1.OA.4.8Determine 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.
This parent flyer and included video can be utilized by both you and parents to build content knowledge and understanding of the strategies highlighted in this unit.
Notes on Assessment:
Use Chapter 5 Go Math Assessment
Form B
The performance task should be given after GCG 1
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:More Addition and Subtraction Strategies
Students will use choose two numbers that will equal a given sum, draw a model, and write related facts sentences.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 (Click to view PowerPoint in slide show mode): Related Facts
Using related facts to solve addition and subtraction strategies / Projected Time Allotment:5 days
Sample Essential Questions:
Day 1:How do related facts help you find the missing number?
Day 2:How do you find related addition and subtraction facts in a fact family?
Day 3:How do you know if addition and subtraction facts are related?
Day 4:How can you use the relationship between addition and subtraction to help you solve problems?
Day 5:How can use number bonds to help you identify the missing number in a fact family?
Related Unit 5 Assessment:Go Math #3-8, 11-12, 16-17
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 to relate addition/subtraction
- Dominoes– Double Nines to make connections to addition and subtraction related facts
- Go Math Lesson 5.2 Essentials:Listen & Draw on p. 189 use different color snap cubes to model related facts, On Your Own on p. 191 with a partner, Problem Solving on p. 192 studentsuse 3 related numbers to identify all of the related facts.
- Voyages Excursion Lesson All Aboard: Use number and operation cards tocreate fact family trains and connect to concrete models representation.
- IlluminationsFinding Fact Families:Children listen to a story and write the related subtraction sentence for each page. Then find a domino with that many spots in order to write the related addition equation.
- Go Math Lesson 5.3 Essentials: Share and Showp. 194 to be used as a check for understanding.
- Go Math Lesson 5.5 Essentials:Listen & Draw on p. 201 use snap cubes to model the problem, Problem Solving on p. 204 have students share their strategy for solving each problem. Problem solving scenario as exit ticket.
- Go Math Lesson 5.6 Essentials:Share and Showp. 206 introduce how to use number bonds and make connections to related fact (triangular flash cards), On Your Ownp. 207 complete independently.
- iTools: Counters
Sample HOT Questions:Select or create appropriate questions to facilitate student discussion.
- 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 better 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 sentence 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 (Click to view PowerPoint in slide show mode): Operations and Equations
Understand the meaning of the equal sign and determine if the equations are true or false / Projected Time Allotment:
5 days
Sample Essential Questions:
Day 1:How can you use addition to check subtraction?
Day 2:How do you choose when to add and when to subtract to solve a problem?
Day 3:How can you use a balance to solve for an unknown number?
Day 4:How can you decide if a number sentence is true or false?
Day 5:What is the meaning of equal sign and how do we use it in number sentences?
Related Unit 5 Assessment:Go Math Ch. 5 #1-2, 13-15, 20-21
Instructional Resources
Manipulatives:
- Snap Cubes — use two different colors to show the part-part whole relationship
- Two-Colored Counters—Model problem situations involving addition and subtraction
- Pan Balance—label the center with the equal sign to demonstrate “equal to” or “same as”
- Operation Cards—use to help students orally read the number sentences correctly
- Go Math Lesson 5.4 Essentials:Listen & Draw on p. 197 discussion on if a situation is addition or subtraction based on context and how they relate. Change Unknown Problem Solving cards to act out the problem and make connection how to use addition to subtract.On Your Own on p. 199as a check for understanding.
- Go Math Lesson 5.7 Essentials:This entire lesson p. 209-212 focuses on understanding what operation is being modeled in a situation. It is important that students are making connections to what is happening in context of the problem and NOT key words.
- Voyages Excursion Lesson:Balance Mechildren become familiar with using a balance to a model of an equation and learn to read and solve number sentences with one unknown addend.
- Go Math Lesson 5.9 Essentials:Listen & Draw on p. 217 to build models to determine if number sentences have the same value, On Your Own and Problem Solving p.219-220 determine if equations are true.
- Dana Center Early Mathematics Resource Lesson 10:Understanding the Equal SignThis lesson focuses on equal meaning the same as regardless of context and determines if an equation is true or false.
- iTools -Primary Algebra Number Balance
- DreamBox Learning Math Lesson Build Expressions Equal to Twenty
- Mega Math Country Countdown, Counting Critters:Level T, Level M, Level H
Sample HOT Questions:Select or create appropriate questions to facilitate student discussion.
- 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 better able to…
- Construct viable arguments, use precise language and critique the reasoning of others. (SMP 3and 6)
- Understanding the various strategies and use tools when solving problems. (SMP 1 and 4)
- Build equations to represent a problem and use strategies to determine if equations are true or false. (SMP 2)
- 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 through exploring 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 (Click to view PowerPoint in slide show mode): Ways to Make Numbers within 20
Use addition and subtraction strategies to find different ways to make 20, and relate subtraction to addition. / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1:How can making a model help you solve a problem?
Day 2:How can you add and subtract in different ways to make the same number?
Day 3:How can addition and subtraction strategies help you find sums and differences?
Related Unit 5 Assessment: Go Math Ch. 5 #9-10, 18-19, 22-24
Instructional Resources
Manipulatives:
- Two-colored Counters—Model addition and subtraction problem
- Snap Cubes — Use to represent bar models in problem solving situations
- Dominoes/Dot Cards Teacher Resources BLM 19-20— Children work in pairs to write related addition facts to build fluency within 20
- Go Math Lesson 5.1 Essentials: This entire lesson p. 185-188 focuses on understanding the problem solving process through building bar models, this helps children to see what part of the problem to find.
- Go Math Lesson 5.8 Essentials: Use ideas shown on p. 213 – 216, but make engaging for students to show different ways to make numbers within 20 by using number cards, multiple representation posters, number webs, etc.
- Go Math Lesson 5.10 Essentials: Share and Showp. 222 assign small groups of student 5 problems each to solve independently, after complete have students work in small group to share strategies used,Problem Solving p. p.224 on their own to check for understanding.
- Primary iTools—Snap Cubes
- DreamBox Learning Math Lesson Build Expressions Equal to Twenty
- FASTT Math— settings Addition 0-9
- Mega Math, Country Countdown, Counting Critters, Level U
Sample HOT Questions:Select or create appropriate questions to facilitate student discussion.
- 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 better able to…
- Construct viable arguments and critique the reasoning of others.(SMP 3)
- Solve problems and analyze mathematical relationships to draw conclusions. (SMP 1 and 4)
- Add and subtract within 20 with precision. (SMP 6)
- Facilitate discussion among students to use precise language in arguing and critiquing. (SMP 3)
- Provide opportunities for students to read and listen to problems and explore building equations and models. (SMP 1 and4)
- Hold students accountable foruse precision when adding and subtracting within 20. (SMP 6)