1. Problem Structure: Putting Together/Taking Apart
Unit of Study: Addition and Subtraction Concepts
Global Concept Guide: 2 of 5

2. Content Development
This global concept guide focuses on two problem structures: put-together and take-apart within addition and subtraction.
These two problem structures differ from the first two structures (add to and take from). Now, students will focus on joining two groups or separating one group. Previously, students focused on situations that added to one group or subtracted from one group.

3. Content Development- Bar Model
Commonly used strategies include making a list, looking for patterns, working backwards, solving a simpler problem, acting it out, and guess & check. However, of the many problem-solving strategies students learn, perhaps the most logical, thorough strategy is bar diagramming.
Bar diagrams (also known as a bar model):
Helps students visualize situations.
Create concrete pictures from words and abstract situations.
Demonstrate comprehension of the problem.
Lead students to a viable solution plan.

4. Content Development Cont.
Bar diagrams connect problem solving from one grade level to the next. With the continuity of a common method used across different grade levels, students can utilize this strategy with confidence.  
Bar diagrams clearly align with the four-step problem-solving plan.
Students create a visual representation to demonstrate a clear understanding of the problem.
The bar diagram requires students to identify the problem’s setting and the values associated with the situation.
The completed bar diagram leads to a definitive solution plan.
The bar diagram can be used as a visual clue to determine the reasonableness of the solution
Silbey, R. Bar Diagrams: The logical, visual problem-solving strategy. Downloaded from on June 12, 2013

5. Content Development- Bar Model

6. Content Development- Bar Model

7. Content Development- Bar Model

8. Day 1
Essential Question: How can you represent put-together and take-apart in problem situations?
Conceptual Understanding
Early Mathematics, Session 6 Lesson: Put Together/Take Apart Problems (Addend Unknown) - This lesson focuses on the missing addend within an addition or subtraction problem situation. It is essential for students to continue building understanding about the concept of addition and subtraction.
Go Math Lesson 1.3 Essentials: Listen & Draw on p.21 to have students model put together problem, Share and Show on 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 use as a problem solving task to further explore patterns with two addends unknown.
By the end of Day 1, students should be able to use manipulatives to directly model put-together and take-apart problems.

9. Day 2
Essential Question: How do number patterns and structures help me solve for missing parts?
Conceptual Understanding
Early Mathematics, Session 7 Lesson: Add-To/Take From Problems (Both Addends Unknown) - In this lesson, students need to understand the relationship of the two addends. If one addend’s value increases the other addend’s value decreases. This pattern structure is an essential understanding of addition.
The following anchor chart can be used with session 7. It can be used to show the relationship between two missing addends. It is important for students to discover the pattern between the two addends. Teachers should carefully select student models to allow for discovery of the pattern.
Go Math Lesson 2.3 Essentials: Problem Solving on p. 64 #9 children can use creative thinking and context clues to find the parts.
By the end of Day 2, students should be able to use their understanding of number patterns to find multiple possible answers for given problems and justify their thinking.

10. Day 3
Essential Question: How does a bar model help you represent a problem?
On day 2, students explored addition and subtraction situations with two missing addends. Connect this exploration and learning with the bar model represented in Lessons 1.4 and 2.4.
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 Problem on 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.
By the end of Day 3, students should be able to use a bar model to find/record the solutions to different take-apart and put-together problem solving scenarios.

11. Enrich/Reteach/Intervention
Go Math: Chapter 2 p. 61B Tier 1- Students will model problem situations and the teacher will provide guiding questions to support learning.
Go Math: Chapter 2 p. 65B Tier 1- Students will draw a bar diagram/model to represent the situation.
Go Math: R4 Model: Part-Part-Whole- Students will have the opportunity to extend the learning to the bar model/diagram.
Go Math: R15 Model Part-Part-Whole- Students will have the opportunity to extend the learning to the bar model/diagram.
Enrich- These enrichment lessons allow student to focus on the bar model.
Go Math: E12 What’s for Lunch-Students will solve subtraction word problems using a model.
Go Math: E4 Complete the Bar Model-Students will use the bar model to solve word problems.
Enrich/Reteach/Intervention