Math Workshop 11/8 Practicum Ms. Harrington & Mr. Aspinwall Tyrell & Isabella
Objective of Lesson:
Ensure students have access to and understand multiple strategies for multi-digit multiplication.
Ensure students have the ability to explain multiple strategies to peers.
Standard(s) Assessed:
5.AT.1: Solve real-world problems involving the multiplication of whole numbers.
Standard(s) Addressed:
PS.1: Make sense of problems and persevere in solving them.
PS.3: Construct viable arguments and critique the reasoning of others.
4.C.7: Show how the order in which two numbers are multiplied (commutative property) and how numbers are grouped in multiplication (associative property) will not change the product. Use these properties to show that numbers can be multiplied in any order. Understand and use the distributive property.
4.AT.3: Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7, and 7 times as many as 5). Represent verbal statements of multiplicative comparisons as multiplication equations.
This lesson is about multiplication of whole numbers but there are significant connections that are made to the 4th grade standards. There are times where connections will have to be made with what multiplication is as ___ groups of ____. The other important key is the two numbers being interchangeable, for example, 3 groups of 4 is the same as 4 groups of 3. Ultimately students will need to persevere through these problems and communicate with one another about why they solved it a certain way. This is how these other standards are addressed.
Mini-Lesson
Connection:
We’ve been working on multiplication.
Last week both students showed strengths with one strategy that was familiar to them.
Teaching Point:
Mathematicians use and can explain a variety of strategies when solving problems.
Active Engagement:
Show a sheet with a variety of strategies solving the multi-digit multiplication problem 12 x 15, including the two that Tyrell and Isabella are most comfortable with, and explain how they work (area model, ratio table, grouping)
Tyrell and Isabella will solve 12 x 15 on their own using all three strategies that are shown on the sheet.
Link:
As you work on today’s problem, use a variety of strategies and be prepared to explain them.
Independent Work
Student Activity:
Choosing between 3 different problems of varied difficulty solving and explaining them mathematically with at least two strategies.
Problems: 14 x 16, 54 x 38, 382 x 18
Solve one of these problems in at least two ways, being able to show your work and explain your strategy
Once finished, you can move on to the next problem listed, go at your own pace**
** Independent Work Commentary: Tyrell wanted to try the traditional algorithm and was not able to finish the problem; we encouraged him to not feel obligated to use that method if he was not comfortable with it yet (shown in top right photo). In the bottom left photo, you can see that Tyrell used the repeated addition method that he loved (and continued to use throughout our lesson- what a win!) but he had trouble keeping track of his numbers. We suggested that he draw lines to separate out his “grouping” and that helped him a lot with his organizational issues. He continued using the box method which he is (and always has been) extremely comfortable with (shown in the bottom left photo) and he was able to adequately solve and explain his reasoning for the problem. He also did a remarkable job implementing the ratio table that we introduced to him at the beginning of the lesson (shown in the bottom right photo) and even got curious about switching out some of the numbers that he had modeled for ones that made more sense to him.
Conferring:
Tyrell and Isabella will be explaining their strategies to each other in hopes that they are able to learn from one another.
Small-Group Work:
Tyrell and Isabella will work together or independently on the problems but will come together to discuss their use of strategies.
Group Share
Teaching Point:
Mathematicians use and can explain a variety of strategies when solving problems.
Anticipated Focus of Conversation:
“After today, do you both feel confident in your ability to use at least two strategies and explain them?”
Reflection *Only Tyrell was present today*:
• Students’ Strengths – strategies, math concepts, standards, etc. (be specific about as many students as possible):
Tyrell did a great job today with the area model strategy as well as the repeated addition strategy. He was able to implement these strategies in all aspects of the problem (as shown in the photos above). He was able to use multiple strategies in solving multiplication problems in order to meet the standard. Tyrell is strong in his use of the area model strategy and the repeated addition strategy and is becoming increasingly proficient in the ratio table strategy as well- he is showing great progress and we are confident in his ability to master these strategies in the weeks to come.
• Students’ Needs – strategies, math concepts, standards, etc. (be specific about as many students as possible):
Although Tyrell understood the strategies when we initially explained and worked through them together, he had difficulty implementing some of them on his own. Tyrell values speed and mental math rather than taking his time to get the right answer each step of the way. Tyrell needs more practice in order to fully meet the standard and become proficient in all strategies. More specifically, in terms of practice, we want to encourage Tyrell to take his time and truly understand the math that he is doing. Oftentimes, we believe that Tyrell is trying too hard to rush through these problems, and due to that, he is missing the overall concepts and methodology behind these strategies.
• Plan of Action – strategies, math concepts, standards, partners, etc. (be specific about as many students as possible):
It is going to be a little different next time with Isabella also incorporated into the dynamic but the approach is going to be largely the same. Tyrell needs more practice in solving problems properly and taking his time with the different strategies, while Isabella needs the work we have done today. It will be working from behind in a sense for Isabella but Tyrell is still working on the same strategies. For next week, we will essentially keep the lesson the same for Isabella and use this as a “review” for Tyrell as well as scaffold Tyrell’s learning by letting him move on to independent practice after the initial active engagement review and give more attention/help to Isabella as she is still in the first stages of learning these strategies. (Plan of action shown in next lesson plan) *Change the numbers in the active engagement problem so that it’s new to both Tyrell and Isabella to work through. *Give BOTH students the new independent practice problems so that they can collaborate
• My Strengths as a Teacher – attend to as many of the 8 Effective Practices as possible:
Our strengths as teachers played extremely well together to build a strong and dynamic team. We were able to establish the mathematical goals to focus the learning from the get-go by getting Tyrell to practice each of the strategies during our “active engagement” section and we introduced this as his learning goal because we emphasized the importance of using and explaining multiple strategies (Effective Practice #1). As previously stated, we then had Tyrell move on to independent practice problems where he was able to put these strategies into practice in order to promote both reasoning and problem solving (Effective Practice #2). Tyrell used and connected mathematical representations that were initially introduced in our active engagement in his independent practice, he was using strategies that he became familiar with earlier in the lesson which was awesome to see (Effective Practice #3). Lastly, we continuously posed purposeful questions to entice Tyrell to give us MORE than just the “right answer,” constantly asking him to explain the WHY behind his math (Effective Practice #5).
**Celebration: We knew that Tyrell and Isabella were both interested in anime so we did a bit of background research in order to implement real-life, realistic, and relevant word problems for both of our focal students as well as incorporate their favorite sports (soccer and football). Although this seemed like a no-brainer to us, Tyrell was extremely appreciative and receptive of our implementation of his interests and it truly increased his engagement within his independent practice work time.
• My Needs as a Teacher – attend to as many of the 8 Effective Practices as possible:
For weaknesses, we definitely had trouble with figuring out how to handle Tyrell making small mental math errors during the problems. It was a fine line between stopping him mid-problem and letting him keep going with the right strategy only to end with the wrong answer (Effective Practice #7). Additionally, beyond explaining how he used the strategies we didn’t have a lot of mathematical discourse relating back to the problem and the ‘what we are solving for’ and putting the answer into context (Effective Practice #4). Next week, we hope to improve upon these weaknesses by encouraging Tyrell to explain the math as he goes, allowing us to understand the mentality and reasoning behind the decisions that he is making. As a result of that, we are hoping that Tyrell’s rushed demeanor as well as his mental math mistakes will be limited because he is talking out his thought processes.
8 Effective Practices
Establish mathematics goals to focus learning
Implement tasks that promote reasoning and problem solving
Use and connect mathematical representations
Facilitate meaningful mathematical discourse
Pose purposeful questions
Make the conversation about more than just the “right answer”
Build procedural fluency from conceptual understanding
Support productive struggle in learning mathematics
Elicit and use evidence of student thinking
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