# Day 172: Substitution Puzzles

For the last few weeks I have been using half the period on Fridays to review. A couple of weeks ago I came across some great puzzles at MathArugments180 (the actual credit seems to go to Mimi). These helped students ease back into solving systems by substitution today. I want to also make a note here for next year to use these as a follow up to Noah’s Ark.

A colleague showed me these puzzles about 4 months ago also… I missed out not using ’em earlier.

# Day 98: Substitution

Algebra spent the whole period practicing solving systems by substitution. There are so many different techniques for solving with substitution (solving both equations for a variable, solving only one, distributing, factoring out a common multiple, ect) so we will be spending quite a bit of time here.

The sum of two numbers is 161. Their difference is 35. What are they?

They have had four or five of these so I finally introduced the system of equations method to solving these sorta question. It might have been too soon (Elimination is probably the easiest way to do this). We will come back to them after a bit of practice and hopefully thing will be cleared out.

Systems of equations seem to be a pretty big talking point in the math blogosphere. Let me know if you have come across any great resources on these!

# Day 97: Noah’s Ark

Algebra wrapped up solving systems by graphing today and moved on to substitution. I found an awesome intro activity over at Fawn’s 180 blog.

The first time through, I didn’t give students enough time to chew on the problem. But, for the rest of the day I gave them 20-25 minutes to work on it in small groups. A lot of students were stumped but no one was unable to at least have a start on the problem. I heard a lot of satisfying sighs of relief today after students solved the problem.

With time students came up with a lot of different solutions, I challenged all them and it was a great activity in developing reasoning.

Here are two example of student work

Several students started by assigning values certain animals and set up a system of equations ISH  approach. It was fun hearing their reasoning of how they reached a solution.
The second example lends itself into a smooth transition for a conversation about substitution.

Great day today!