Introduction
Guiding Questions:
How do situations modeled by equations differ from those that can be modeled using inequalities?
What are some other ways that you could represent the problem?
Where do you see the quantities in a real-world situation represented in the equation/inequality?
Florida's State Standards:
Students apply concepts and skills related to benchmark MA.912.AR.2.1
Given a real-world context, write and solve one-variable multi-step linear equations AR.2.1
Apply mathematics to real-world contexts; Students apply mathematical concepts previously learned to develop a model representing real-world scenarios. Students interpret solutions and analyze as to why the modeled solution may differ from the real-world answer. MA.K12.MTR.7.1
Students also engage in representing and connecting and the reasonableness of solutions. In testing their models, students look fo patterns in the structure of their models. MTR.2.1.MTR.6.1.MTR.5.1
Task
Watch an assigned video on a contest held by a teacher to see which student collects the most cans and how four students keep track of how many they each collected.
Process
Step 1: Play the video
- The video shows four friends who collected cans for the contest. Each friend has cans in a bag, but we cannot tell how many cans are in each bag.
- Have my students brainstorm from the main question: How many cans does each friend have?
Step 2: Modeling with Math
- As students ask, use the video to provide information about the number of cans each friend has and pause after each statement: Angela has three times as many cans as Brian. Brian has four fewer cans than Carlos. Carlos has twelve cans. Danielle has fewer cans than anyone. All cans are the same size. All cans are in the bags, and each bag has only cans in it. All four statements are accurate.
- Give students time to think about how their ideas are connected to what they learned in this topic about writing and solving equations and inequalities. Students may use a,b,c, and d as variables.
- Within this step, students will be split into designated pairs to work on creating an equation and an inequality for the problem.
Step 3: Play the final video
- Before playing the video, review as a class what each pair concluded as their equation and inequality. Take note of those who got the closest to what the video will tell us.
- Main question answer: Angela has 24 cans, Carlos has 12 cans, Brian has 8 cans, and Danielle has 5 cans.
- "Post-game" analysis: ask students about other possibilities for the number of cans that would work for the situation.
Step 4: Self Challenge
- Have one of the two students from each pair move and pair with the residing student pair and challenge the new pairs of students to construct their problem.
- Their problem must include a certain number of friends, cans, and clues. The new pair must write one equation and one inequality.
Evaluation
| Criteria | Exceptional: A (8-10 points) | Proficient: B (6-8 points) | Meets Expectations: C (3-6 points) | Failing: F (03 points) |
| Content | Students clearly understand and are capable of using critical-thinking skills to create an equation and inequality using all required elements: number of friends, cans, and clues (need to have at least 5 clues). Students were creative and actively communicated respectfully to work as a team to complete the assignment. | Students have an understanding of the assignment and were able to use their critical thinking skills to write at least one inequality and one equation, yet missed or misused a required element. | Students understand the assignment, yet do not use critical thinking to create an inequality or equation. Students were not creative or communicating within their designated pairs. Students missed and/or misused at least two of the required elements and had less than 5 clues needed. | Students did not have a clear understanding pf the assignment. Students were not able to use critical thinking skills to write one inequality and one equation corresponding to the assignment. Students missed and misused all elements. Students were not creative nor communicating within their designated pairs. |
Total: /10
Students will be evaluated as pairs. Points will be taken off if students communicate with peers who are not in their designated pairs or if caught cheating/ taking other pair's problems.
Conclusion
Students were provided an activity based on a video provided regarding can collection and were assigned to work in pairs to write one inequality and one equation to solve the problem related to the video. A supplemental resource that can be used is the Desmos scientific calculator to aid in solving complex multiplication, division, addition, or subtraction.