## Ties and Suspenders.doc - Section 2: Investigation

# REVIEW: Systems Review and Word Problem Practice

Lesson 12 of 17

## Objective: SWBAT solve real world problems using systems of equations.

## Big Idea: Students have the opportunity to review and practice solving systems of equations, including those with inconsistent and dependent systems

*60 minutes*

#### Opening

*25 min*

I begin today's class by explaining to students that the purpose of today’s activity is to give them an opportunity to practice solving systems of equations, especially as they relate to word problems. I let them know that before they get to today’s problem, they will warm up by solving three systems of equations. They will work on the systems review warm up individually and when finished, try to come to a consensus about the answers in their groups or at their tables.

I plan to have students present their answers on the second warm up problem (an inconsistent system) and the third warm up problem (a dependent system). I try to get students to articulate the difference between the two systems.

- How do you they know that one system has no solution and the other has an infinite number of solutions?
- How could they check their work?

This is a great opportunity to ask students what the graphs of these systems would look like and help them connect the algebraic method to the graphing method.

#### Resources

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#### Investigation

*30 min*

Students are now ready to try today’s word problem:

They are welcome to work alone, with a partner, or in a small group. I find this to be a good opportunity to offer student choice. I circulate to check for understanding and provide guidance. If there is time during this section, I have students share out their answers and the different methods they used to solve the problem and how they connect. I make sure students do not stop working once they have found the number of ties and the number of suspenders. This problem requires them to use this information to find out how much money will be on the gift card from the online retailer.

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#### Closing + Homework

*5 min*

Today’s reflection should focus on students considering their own improvement. On an index card, I ask students to write about three ways this work shows s/he has improved.

**Homework**: There is an opportunity to assign differentiated homework at the end of this lesson. Students who have mastered solving systems of equations and who worked through the word problem easily can go on to the extension problem. Students who still need to practice the mechanics of solving systems can work on some practice problems. Students who need more work translating word problems into systems of equations can work on some word problem practice.

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- UNIT 1: Introduction to Algebra: Focus on Problem Solving
- UNIT 2: Multiple Representations: Situations, Tables, Graphs, and Equations
- UNIT 3: Systems of Equations and Inequalities
- UNIT 4: Quadratics!
- UNIT 5: Data and Statistics
- UNIT 6: Arithmetic & Geometric Sequences
- UNIT 7: Functions

- LESSON 1: Introduction to Inequalities: Working with Constraints
- LESSON 2: Emerging Pictures: Graphing Inequalities in Two Variables
- LESSON 3: Two Methods, One Equation: Finding the Boundary Line
- LESSON 4: Writing and Graphing Inequalities to Represent Constraints
- LESSON 5: Finding the Feasible Region
- LESSON 6: Where Do the Lines Cross?
- LESSON 7: Solving Systems Using Elimination: An Intuitive Approach -- Day 1 of 2
- LESSON 8: Solving Systems Using Elimination: An Intuitive Approach -- Day 2 of 2
- LESSON 9: Introducing Inconsistent & Dependent Systems
- LESSON 10: Finding the Feasible Region: From Start to Finish
- LESSON 11: Maximizing Profit: An Introduction to Linear Programming
- LESSON 12: REVIEW: Systems Review and Word Problem Practice
- LESSON 13: SUPPLEMENT: Linear Programming Application Day 1 of 2
- LESSON 14: SUPPLEMENT: Linear Programming Application Day 2 of 2
- LESSON 15: ASSESSMENT PROJECT: Writing Linear Programming Problems Day 1 of 3
- LESSON 16: ASSESSMENT PROJECT: Writing Linear Programming Problems Day 2 of 3
- LESSON 17: ASSESSMENT PROJECT: Writing Linear Programming Problems Day 3 of 3