Embedded Files
Currently, in Collin’s math class, the teacher has begun instruction regarding MA.4.NSO.2.2 (Multiplying two whole numbers, up to three digits by up to two digits, with procedural reliability). He has struggled to develop skills necessary to multiply effectively and efficiently such as memorizing basic multiplication facts.
Collin’s teacher worked out problems on the whiteboard, modeling the use of a zero as a placeholder and verbalizing how she solved the problem.
She then provided Collin’s class with a worksheet of 15 similar problems for them to work out.
Collin had difficulty with correctly lining up the problem and repetitively got incorrect answers. He was also very overwhelmed with doing worksheets. The way that Collin’s teacher was providing instruction was not ensuring success for him. She noticed that he would disengage and begin doodling on other papers.
Guiding Questions:
What could allow Collin to be able to access the instruction?
What could allow Collin to better apply and transfer knowledge with mathematical concepts?
How could Collin demonstrate his learning in other ways?
Redesign
Within her problem solving and instructional planning, Collin’s teacher 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 learning.
She now provides options for students to access instruction to decrease difficulty with number sense and operations. For example, she models using an area model, thinking aloud for students to hear the steps for solving the problem.
Area Model
She also models during instruction using concrete and virtual manipulatives. For example, students can explore multiplication of multi-digit numbers using area models (such as above) and manipulatives (concrete and virtual) to develop procedural fluency and procedural reliability.
Base Ten Blocks
Mathigon's Polygon
Collin’s teacher provides options for students to engage in one of the activities below during Centers.
Center 1 (B1G-M Instructional Task): Paul orders tomatoes for The Produce Shop. Each box has 24 tomatoes in it. If Paul orders 32 boxes of tomatoes, how many tomatoes will The Produce Shop have to sell? Use a strategy of your choice to find the number of tomatoes The Produce Shop has to sell. Explain your thinking and why your method works.
Center 2 (B1G-M Instructional Item):
The product of 57 and 92 is _____
a. 627
b. 4,644
c. 5,234
d. 5,244
Center 3 (Small group with teacher): Teacher provides explicit instructions on multiplying multi-digit numbers by modeling a problem. Students take notes and solve problems with a graphic organizer.
Center 4 (Kahn Academy video): The video can be paused, replayed, etc. for those who need repeated viewing of the concept.
Center 5 (Toy Theater): Website to review and practice concept.
Finally, she provides a variety of options for demonstrating learning, other than solving by using the standard algorithm. This decreases the possibility of applying strategies inconsistently and losing place when working out problems abstractly. For example, all students had the following options:
Complete a worksheet of 10 multi-digit multiplication problems.
Create a representation, using a graphic organizer, of a real-world problem involving multiplication of two multi-digit numbers.
Create a model using base-10 blocks (or another manipulative).
Students complete an interview with the teacher explaining and showing (through their choice) how to solve the problem.
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