# 4-Digit in Algebra 1

Day 3, Fri Aug 15, 2014

The Brain Surgeon: My third Growth Mindset Vehicle (after the Drumroll and the Wrinkle Sprinkle) is the Brain Surgeon. I purchased a soft foam model brain (it comes in two hemispheres). Each day, I give it to the next student in line and that student is the Brain Surgeon for the day. The Brain Surgeon has two Primary responsibilities: To lead both the Drumroll and the Wrinkle Sprinkle. The two secondary duties are to make sure that materials (portfolios, whiteboards, chromebooks, graphing calculators etc) get disseminated and collected properly.

Our First Brain Surgeon:(Jasmin)

Target: We will use Order of Operations and Quantitative Reasoning to write expressions for a given value.

SMP #2, Reasoning Quantitatively: I intend to use my MPJ Practice Posters to introduce each of the 8 practices within the first few weeks of school. I’m not obliged to go in numerical order; rather I choose the practice that best suits the activity for the day. So today, I gave the students a black-n-white copy of the SMP Posters.

I asked each student to read through the poster quietly. The groups were to have each member share, “Something you already know about the practice, and something that you don’t know.” As a class each group shared out one of each, which I wrote on the board.

While I used the example at the right to describe the difference between contextualize and decontextualize, I let the students know that today we wouldn’t be doing that. Instead, we would being doing a lot of the things that they already know (using numbers, problem solving, evaluating). I found it very interesting that the class conceded to knowing what problem solving meant, but that they did not know how to do it.

The 4-Digit Problem: I shared the rules of the 4-Digit problem, plus the 2 examples, and asked them to create the value 19 with four 8’s. They struggled which resulted in statements like “I feel stupid,” which I was trying to illicit so I could nix that thinking quickly. I shared that they would not have gotten this far if they were stupid. “I believe that you are all smart; I am paid to make you smartER.” I continued, Since they claimed to not know what problem solving looked like, I asked for problem solving strategies.” I just got blank stares. OK, everybody give something with four 8’s, I don’t care what the value. We threw a few up on the board, and discussed some that were close. I shared the hints given in the lesson plan, and let them go at it again. When I revealed the answer, I got a lot of “That’s cool.”

So I asked them to produce values 1-5. They sputtered again, so I asked for just #1. When I showed one example, they all laughed with “It’s that easy?” They were good to go from there…

Wrinkle Sprinkle:

• 8^0 = 1
• It was hard, but fun
• To see it in different ways

# Teaching Order of Ops with the 4-Digit Problem

I teach a low-level Algebra class (Algebra Essentials). Half of the thirty students are Special Ed or English Language Learners. I was teaching Order of Operations, and rather than offer notes on a subject that they had seen several times before (and still failed), I taught the topic with the 4-Digit Problem instead. (created by College Prepetory Mathematic program, UC Davis)

The 4-Digit Problem goes something like this: You must use four of the same digit (I use 8) to form expressions that have designated values. You may use any of the standard operations represented in “PEMDAS;” you may combine eights to make 88; and you may use any number other than 8 only as an exponent (which then makes roots legal). I did offer some hints:
8 ÷ 8 = 1          80 = 1          √(8 + 8) = 4          3√8 = 2.

I had the students practice by first attempting to express the value 19 with four 8’s. I then had them independently attempt to express the values 1-5. Here is what this supposedly low-level group came up. (multiple solutions shown)

1 =  8 ÷ 8 · 8 ÷ 8     or     8 – 8 + 8 ÷ 8

2 = 880 + 880      or     8 ÷ 8 + 8 – 8

3 = 8 ÷ 8 + 80 + 80     or     80 + 8 ÷ 8 + 80

4 = 80 + 80 + 80 + 80     or     8 ÷ 8 · √(8 + 8)

5 = 3√8 + 3√8 + 3√8 – 80

Their class/homework that day was to then generate the values 6-10, and submit for a grade.

Great day for learning Algebra!