Embedded Files
Jared’s math teacher introduced multi-step linear equations last week (MA. 912.AR.2.1 Given a real-world context, write and solve one-variable multi-step linear equations) and he is struggling. He remembers that during 8th grade, he learned about solving linear equations, but he had difficulty and now is also required to write equations.
Jared’s teacher worked out a problem using the whiteboard and verbalized the steps as she went along, such as:
The base rate of renting a car is $36. For every mile that you drive, you are charged $0.10 a mile. If Courtney pays a total of $61, how many miles did she drive? Write and solve the equation to represent this situation.
She then wrote the following problem on the board for the class to solve:
For one month of gym membership, it costs $25. If someone wants to take a group class, it costs $5 per class. If Stephanie pays $75 that month, how many classes did she take.
Jared had difficulty with the problems and repetitively got incorrect answers. He inconsistently applied the properties of equality.
Guiding Questions
What could allow Jared to be able to access the instructions?
What could allow Jared to better apply and transfer knowledge with mathematical concepts?
How could Jared demonstrate his learning in other ways?
Redesign
Within her instructional design, Jared’s teacher now utilizes the cognitive processes and UDL guidelines to ensure that all students have options for accessing and engaging with high-quality math instruction, as well as a variety of ways to demonstrate their learning. She now provides options for students to access instruction in an effort to decrease difficulty by consistently applying the properties of equality. For example, she models the use of manipulatives and a bar model.
Manipulatives
Her instruction includes using manipulatives, such as algebra tiles, to model solving a linear equation. She verbally explains as she writes the steps algebraically. For each step, she identifies the property of equality they could use.
Bar Models (taken from the Algebra 1 B1G-M)
Additionally, she models how to use bar models to represent real-world contexts. For example, Kevin and Fernando have an art project to do. Kevin buys 66 individual markers plus 5 packs of markers. Fernando buys 48 individual markers plus 8 packs of markers. If Kevin and Fernando buy the same total number of markers, how many markers are in a pack?
She uses her document camera to show the problem abstractly and verbally explains the steps as she solves.
Jared’s teacher provides options for students to engage with instruction by incorporating tools and resources in a variety of learning centers.
Center 1 (B1G-M Instructional Task) – City A has a current population of 156,289 and has an annual growth of 146 residents. City B has a current population of 151,293 and has an annual growth of 363 residents. To the nearest year, how many years will it take for City A and City B to have the same populations?
Center 2 (B1G-M Instructional Item) – A group of friends decides to go out of town to a championship football game. The group pays $185 per ticket plus a one-time fee of $15. Each person also pays $27 to ride a tour bus to the game. If the group spent $2,771 in total, how many friends are in the group?
Center 3 (Small group with teacher) – The teacher provides explicit instructions on solving real-world one-variable linear equations by modeling a problem. Students take notes and solve problems with a graphic organizer.
Center 4 (Draw pictures or use bar models) – Students draw pictures or use bar models to represent real-world contexts given a problem on a scenario card.
Center 5 (Desmos Online Software) – Website to review and practice concepts.
Finally, she provides a variety of options for demonstrating learning, other than solving an equation abstractly. This decreases the possibility of inconsistently applying the properties of equality. For example, all students had the following options:
Complete a worksheet of five real-world problems.
Create two real-world scenarios that model given equations.
Create a representation, using a bar model, of three real-world problems.
Solve three real-world problems using algebra tiles.
Complete an interview with the teacher explaining and showing (through their choice) how to solve the problem.
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