"But... Why?"
Knowing algorithms and being able to get the right answer in a math problem is important, but it’s equally important to know the why and how behind how you got there. This lesson focuses on the concept of ‘showing your work’ so that students are working on their math literacy skills at same time that they are ‘doing math’.
Objectives
Students will:
—Solve math problems in a specific strand of math;
—Break a specific math concept down into discreet steps;
—Communicate the reasoning behind a mathematical operation in a clear and concise way.
Standards
This lesson is appropriate for Upper Elementary, Middle School and High School
CCSS.MATH.PRACTICE.MP1
Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP3
Construct viable arguments and critique the reasoning of others.
CCSS.MATH.PRACTICE.MP4
Model with mathematics.
Materials
—Flocabulary Math videos
—Exercise sheet from video page
Time Allotted
1 class period
Sequence
1. Watch a math video, including walking through all of the interactive lyrics throughout the song.
2. Distribute the printable exercises related to the topic to the students.
3. Walk through one problem together as a class.
4. Before completing the rest of the sheet, ask students to take a few minutes on the back of the worksheet to describe in their own words what they are doing when they perform that operation or solve that problem. On the board, write ‘I just do it’ and then put a big line through it explaining that that is not an acceptable answer. If students are struggling, it might be helpful to tell them to pretend that they are explaining it to a child younger than themselves.
5. The explanation can be in words, pictures, diagrams, or any other modality that helps them to communicate the idea behind mathematical process.
Sample
In the three Flocabulary videos about operations with fractions, the hook or chorus of the song offers the quick tip for how to solve each type of problem. These could be shown as a set, and then the questions that can be posed: Why do we treat these problems differently? Why are they flipped sometimes, done straight across other times and even other times done diagonally? What is the reason for that?
Multiplying Fractions:
Multiply across the top, then across the bottom,
Simplify your answer, yep, now you got 'em.
Dividing Fractions:
Keep, change, flip, yeah that’s the action,
Everybody’s gonna know how we’re dividing fractions.
Keep, change, flip, yeah that’s the action,
Everybody’s gonna know how we’re dividing fractions.
Adding Fractions:
Multiply the bottom and the top by the opposite denominator,
Keep the bottom the same, but add the tops,
We aim steady, a-a-adding, if you're ready or not. (x2)
Wrap Up/Extensions
-Have some student volunteers present their explanations to the whole class and walk through them together. As you do this, check in with the rest of the class to see how many students included similar elements in what they wrote.
-As a class, come up with a consensus on a solid explanation for the particular concept or process. Write that up and have it visible in the classroom.
-Optional: Keep a list of the relevant vocabulary that comes up as students do this work. This is a rich word bank to call upon in other math lessons and for test prep.
-Optional: See if there is class that is several grades below your own where students could present their explanation to their younger peers.
Guided Reflection
-"I used to think ______ and now I think ______"
-"One thing I learned is ________________ and one question I still have is _________"