Global Concept Guides: Problem Structure: Add to/Take From, Problem Structure: Putting Together/Taking Apart, Problem Structure: Comparing,Adding in any Order, and Adding and Subtracting All or Zero
Prior Learning: MAFS.K.CC.1.2,MAFS.K.CC.1.3,MAFS.K.OA.1.1,MAFS.K.OA.1.2,MAFS.K.OA.1.5
Progressions Document Link
Show What You Know Task:Go Math Chapter 1 and Chapter 2 Show What You Know (TE p. 10 50)
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.)
Understand and apply properties of operations and the relationship between addition and subtraction.
MAFS.1.OA.2.3Apply properties of operations as strategies to add and subtract.3 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 + 10 = 12. (Associative property of addition.)
Add and subtract within 20.
MAFS.1.OA.3.6Add 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.
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:
Strikethroughs indicate that the primary focus will be to understand addition and subtraction concepts within ten.
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:
Unit 1 is a modified assessment using questions from chapter 1 and 2 form B.
Unit 1 Assessment
See common performance task link below
Performance task to be given after GCG 3
Unpacking the Standards for this Unit:
Many children misunderstand the meaning of the equal sign. The equal sign means is the same as, but most primary students believe the equal sign tells you that the answer is coming upto the right of the equal sign. This misconception is over-generalized by only seeing examples of number sentences with an operation to the left of the equal sign and the answer on the right.
Students may have misconceptions about the meaning of the equal sign.
According to Math Misconceptions, “Simply explaining the meaning of the equal sign is not as effective as providing activities that foster this understanding (p. 56-57).” Students can use balances to help understand the idea of equality. For example, 2 = 1 + 1, 5 + 4 = 3 + 6.
Common Performance Task with Rubric for this Unit:
Students will use their understanding of different problem structures to complete problem solving scenarios.
Click herefor performance task and rubric.
Future learning:
In second grade, students build upon their work in grade 1 in two majorways. (2.OA.1) They represent and solve situational problems of all three types which involve addition and subtraction within 100 rather than within 20, and they represent and solve two-step situational problems of all three types.
1st / Global Concept 1 of 5 for this Unit of Study (Click to view PowerPoint in slide show mode): Problem Structure - Add to/Take From Model addition and subtraction problems in action situations that require adding to and taking away from. / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can you represent adding to and taking from in problem situations?
Day 2: How does the action in the problem help me understand the change that has occurred?
Day 3: What strategies can be used to solve for an unknown part?
Related Unit 1 Assessment:# 1, 2, 4 ,12, 13
Instructional Resources
Manipulatives:
- Snap cubes – use to model action in problem situations for adding on and taking from in all problem types
- Two color counters – use the two different colors to model the problem situations
- Session 3: Add-To/Take-From Problems (Result Unknown)Students use cubes/equations to represent the situations.
- Go Math Lesson 1.1Essentials:Listen & Draw on p. 13 to have students act out the process of adding to, andProblem Solving #7 on p. 16 for more practice adding to with result unknown.
- Go Math Lesson 2.1 Essentials: Listen & Draw on p. 53 to have students act out the process of taking from, and Problem Solving#7, 8 and 10 on p. 56 for more practice taking from with result unknown.
- Session 4: Add-To/Take-From Problems (Change Unknown)Students use cubes/equations to represent the situations.
- Go Math Lesson 1.1 Essentials:Problem Solving#6 on p. 16 to have children interpret the picture.
- Go Math Lesson 2.1 Essentials:Problem Solving #9 on p. 56 to have children analyze the picture to complete a subtraction story.
- Session 5: Add-To/Take-From Problems (Start Unknown)Students use cubes/equations to represent the situations.
- More problem solving situations: including Result, Change and Start UnknownK-5 Teaching Resources
- iToolsCounters– use counters to model problems
- Interactive Whiteboard:Chapter 1 Lesson 1.2 Model Adding To(may need to installActiveInspire)
- MegaMath – Numberopolis, Carnival Stories, A. Addition Stories to 10
- MegaMath – Numberopolis, Carnival Stories, B. Subtraction Stories to 10
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- How can you model adding to and taking from a group?
- How can you determine the action in a problem situation?
- What is another way to represent the action in a problem? (Anticipated student response: I can use a model or an equation to represent action.)
- What strategies can you use to find the unknown information?
- Why should my model match the problem situation?
Our students are better able to…
- Explain strategies used to determine the action in the problem situation. (SMP 1, 3)
- Use precise language to justify thinking (i.e. starting point, change, added to, taking from, equation, model, unknown part). (SMP 6)
- Write equations to represent models. (SMP 2, 3)
- Make connections among the situation, the model, and the equations. (SMP 3, 7)
- Model problems to show action in problems using manipulatives and pictures. (SMP 5)
- Facilitate student understanding by probing for the change or action that occurs in the situations. (SMP 1, 3)
- Develop specific language through modeling and attending to precision in our vocabulary (SMP 6)
- Support the writing of equations to represent the models. (SMP 2, 3)
- Emphasize the connections among the situation, the model, and the equations. (SMP 3, 7)
- Provide problems involving actions and model using manipulatives and pictures. (SMP 5)
1st / Global Concept 2 of 5 for this Unit of Study (Click to view PowerPoint in slide show mode): Problem Structure: Putting Together/ Taking ApartModel addition and subtraction problems in action situations that require putting together and taking apart. / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can you represent put-together and take-apart in problem situations?
Day 2: How do number patterns and structures help me solve for missing parts?
Day 3: How does a bar model help you represent a problem?
Related Unit 1 Assessment:# 3, 8, 10, 11
Instructional Resources
Manipulatives:
- Snap cubes (each student needs 2 colors) to model putting together and taking apart
- Two color counters – use the two different colors to model the problem situations
- Session 6: Put-Together/Take-Apart Problems (Addend Unknown)Students use cubes/equations to represent the situations.
- Go Math Lesson 1.3Essentials:Listen & Draw on p.21 to have students model put together problem, Share and Showon p. 22 for more practice putting together with addend Unknown.
- Go Math Lesson 2.3 Essentials:Share and Show on p. 62 for more practice taking from with addend Unknown.
- CPALMS Formative Assessment – Problem solving task to further discovering of the patterns and structure of two addends unknown.
- Session 7: Put-Together/Take-Apart Problems (Both Addends Unknown)Students use cubes/equations to represent the situations.
- Go Math Lesson 2.3 Essentials:Problem Solving on p. 64 #9 children can use creative thinking and context clues to find the parts.
- Go Math Lesson 1.4 Essentials:Unlock the Problem on p. 25 to have children solve an addition problem using a bar model, #1-6 on p. 26 – 27 for more practice adding using a bar model.
- Go Math Lesson 2.4 Essentials: Unlock the Problemon p. 26 to have children solve an problem using a bar model, #1-6 on p. 66 – 67 for more practice subtracting using a bar model.
- iToolsCounters– use counters to model problems
- MegaMath – Numberopolis, Carnival Stories, E. Missing Addends to 10
Sample HOT Questions:Select or create appropriate questions to facilitate student discussion.
- How do the parts in the equation connect to the model?
- Is there another way we can represent this situation with an equation? Explain.
- Explain how the bar model changes when you increase the first addend in an addition problem.
- Explain how the bar model changes when you decrease the first addend in an addition problem.
Our students are better able to…
- Use precise language to justify thinking (SMP 6)
- Model problems to show putting together or taking apart with manipulatives and pictures. (SMP 5)
- Writing equations to represent models. (SMP 2, 3)
- Looking at the relationship between addends to show that when one addend’s value increases the other addend’s value decreases. (SMP 7)
- Develop specific language (i.e. put together, take apart, addend, equations, bar model, structure, and pattern). (SMP 6)
- Provide multiple opportunities and tools to model problems. (SMP 5)
- Support the writing of equations to represent the models. (SMP 2, 3)
- Probe for student discovery of the pattern between the value of the addends and select student models to share that allow for this discovery. (SMP 7)
1st / Global Concept 3 of 5 for this Unit of Study (Click to view PowerPoint in slide show mode):Problem Structures: ComparingModel addition and subtraction problems in comparing situations. / Projected Time Allotment:
3 days
Sample Essential Questions:
Day 1: How can you use manipulatives to compare two numbers?
Day 2: How can you use pictures and models to compare two numbers?
Day 3: How can we use different strategies to compare two numbers?
Related Unit 1 Assessment:# 6, 14, 18
Instructional Resources
Manipulatives:
- Snap Cubes –Represent two numbers by creating trains which can then be placed next to each other and compared
- Two-colored counters –Use the two-color counters next to each other to show the one to one correspondence of each set
- Number lines –Used to show the difference between two numbers.
- Session 8: Compare Problems (Difference Unknown)Students use cubes/equations to represent the situations.
- Illuminations- Comparing Connecting Cubes- model a subtraction problem in which two sets are compared and write the equation to match.
- Go Math Lesson 2.5 & 2.6–Complete lessons can be used to help realize comparison subtraction. It is important to make the connection between using manipulatives and showing problem in a quick picture.
- Voyages 1st Grade Excursions: Compare- Children will find out how much greater or less than one number is than another by using direct comparison, counting on, and using subtraction
- Animated Math Models- Skill 9(Subtract to Compare)
- iTools Counters – use counters to model problems
Sample HOT Questions:Select or create appropriate questions to facilitate student discussion.
- How can we represent the following problem with snap cubes?
- How could you use both addition and subtraction to represent this problem?
- How could you represent this problem with a number sentence?
Our students arebetter able to…
- Verbalize how they utilize manipulatives, pictures, and models to compare two numbers. (SMP 2, 3)
- Compare and contrast their model and another student’s model, in particular, the use of addition and subtraction strategies for the same problem. (SMP 3, 7)
- Use precise language to justify thinking (i.e. less, fewer, more, difference, compare, model). (SMP 6)
- Encourage students to use different models and communicate how they directly compare two amounts. (SMP 2, 3)
- Help students see the natural connections between using subtraction to compare and the related addition comparisons (missing addends). (SMP 3, 7)
- Develop specific language through modeling and attending to precision in our vocabulary (SMP 6)
1st / Global Concept 4 of 5 for this Unit of Study (Click to view PowerPoint in slide show mode): Adding In Any OrderExplore Commutative Property of Addition / Projected Time Allotment:
2 days
Sample Essential Questions:
Day 1:Why can you add addends in any order?
Day 2:How can the commutative property help me solve a problem?
Related Unit 1 Assessment: #5, 15, 17
Instructional Resources
Manipulatives:
- Snap Cubes– Build model of addition sentences to show each addend and how it can be turned around to model the commutative property.
- Go Math Lesson 1.6Essentials:On Your Own on p. 35 #4-9 to identify addition sentence that use the commutative property, Problem Solving on p. 36 # 10-13 students can make connections between picture and numbers sentences.
- Turn Around Trains– Build snap cube trains as a hands-on alterative activity for p. 34.
- Commutative Property Lesson – Part One steps 1-5 on pages 2-3 to be used as an engage
- Go Math Lesson 1.7Essentials:Listen & Draw on p. 37 use snap cubes to explore all the different ways to make 5, On Your Ownon p. 39 #11-21 to help students make an organized list and connect to the commutative property, Problem Solving on p. 40 #22-23 to demonstrate higher order thinking.
- Making Ten – This is an additional resource that uses snap cubes to show the relationship between making a ten and the commutative property.
- Grade 1 Animated Math Model- Skill 4 (Add in Any Order)
- iTools- Counters/Number Balance (Algebra)
Sample HOT Questions: Select or create appropriate questions to facilitate student discussion.
- How can different strategies be helpful when solving a problem?
- Dante says that if 8-2=6 is true, then 2-8=6 must also be true. Do you agree or disagree with Dante’s thinking? Why or why not?
- Explain what the equal sign tells us? (Anticipated Responses: Students should understand that the equal sign tells us that both sides are the same value. A common misconception is that the equal sign means the answer is coming.)
- How does knowing 6+2=8 help you answer 2+6?
- Molly was excited. She said "Look what I found out, 2+4=6 and 4+2=6." "Molly said, "I can show you why that works." Describe what Molly did.
Our students are better able to…
Methodically find all the combinations for a sum.(SMP 7)
Use the understanding gained through hands-on activities to create a definition of the Commutative Property in their own words. (SMP 5, 8)
Use precise language to justify thinking (SMP 6)
For more info on SMP’s click here. / Because as teachers we…
Provide explorations in structure by finding all the combinations of a sum. (SMP 7)
Provide hands on opportunities and facilitate discussion on the meaning of the equal sign and the order of addends. (SMP 5, 8)
- Emphasize use of correct vocabulary: addends, sum, and order. (SMP 6)
1st / Global Concept 5 of 5 for this Unit of Study (Click to view PowerPoint in slide show mode): Adding and Subtracting All or Zero
Explore what happens when adding or taking away zero, and taking away all. / Projected Time Allotment:
2 days
Sample Essential Questions:
Day 1:What happens when you add zero to a number?
Day 2:What happens when you subtractall or zero from a number?
Related Unit 1 Assessment:# 7, 9, 16
Instructional Resources
Manipulatives:
- Counters – used to model adding and subtracting 0 in different problem scenarios
- Go Math Lesson 1.5Essentials: Start with Access Prior Knowledge TE p. 29 to be able to show the difference between adding something and adding nothing, Listen and Draw on p. 29 to have students act out the process of adding 0 to a number, Share and Showon p. 30 to model using dominoes, Problem Solving on p. 32 # 18, 20-21 to understand zero means the same as none.
- Go Math Lesson 2.7Essentials: Listen and Draw on p. 77 use counters to model and draw subtracting zero and subtracting all, On Your Own on p. 79 #7-18 completing subtraction sentences to find the difference, Problem Solving on p. 80 #21-22 requires students to use higher order thinking skills
- Animated Math Model- Skill 3 (Add Zero)
- Animated Math Model- Skill 10 (Subtract All or Zero)