It is time to take a short quiz to see if students understand how to group, make arrays and create equations based on those pictures. I decided to do a short whiteboard review and go over a sample of each type of problem we had been working with in the last couple of days.
I listed the number 32 on the board and asked them to explain how we go about finding factor pairs.
One boy raised his hand and said that we should start with 1x something and continue. So, I listed the first pair. Once we got to 2 x, another boy suggested that we probably need to make an array to figure that out.
I asked if it was divisible by two?
They all yelled yes! And so I quickly set out making the array until we had 32.
Then, one girl said that we could circle the "quick array." The quick array is simply circling one row and one column that would be the factor pair. So, I honored her request and circled the quick array. I circled the 2 dots running vertically x 16 dots horizontally in the array as it was listed for the next pair. That defined the "quick array". We call it "quick" because it shows the portion of the array that would give us the product if we multiply them together. It is used for more advanced students who still want the visual model, but know the factors. I accept this shorter version of the array for those who have mastered their facts as a way of proving their understanding. As I had hoped they will use this strategy when they get stuck! Sometimes just drawing out that many dots helps trigger their factor memory!
I asked about the factor 3 and they agreed it wouldn't work. I always ask "why" after every question and make it a habit so that the conceptual understanding becomes solid. I want it to be a natural part of their math thinking and I am glad that Common Core emphasizes that with the way standards and practices are written.
My question of why was answered well. They explained that 3+2 = 5 and that 5 is not divisible by 3, therefore, three isn't a factor. One boy, who knows his facts really well was getting impatient and told us that 4 x 8 is 32 and that the "turn around" would be 8 x 4. In other words, let's get moving. It I can take a hint and promptly finished up the listing, but not without holding everyone accountable for explaining why 5,6 and 7 aren't factors.
We reviewed the Commutative Property together. I listed a x b=b x a.
I then drew 5 circles with 3 dots and asked them to give me an equation for the picture. Immediately, they responded with 5x3. I asked why it isn't 3x5? I called on one student and he explained that it was five groups of three. I drew out 3 groups of five so they could see the difference.
I then drew an array of 5 rows and 6 columns. I asked them what factor pair described this array. A student who really struggles said, it's 5 across and 6 up and down.
I asked what they thought if it went the other way and I drew it as 6x5. They remembered. I pointed to the factor pair cards along the wall and asked that they remember that it is rows x columns.
I felt confident that it was time to quiz.
I gave my students the quiz and read the directions out loud so that they understood what was expected. I think it is important to go over the directions because in #1 & #2 there are two parts; equation writing and drawing.
I roved the classroom and noticed that the first problem was revealing as far as understanding what the equation meant. This quiz reveals the understanding if they can create an equations that mean "groups of n". I was seeing some confusion in number 1.
I noticed that my lowest reading student was struggling with the directions. I stopped and went over them with her again and had her move to a less distracting place in the room. I let my students take quizzes either at their desks or around the room. This ensures that they are comfortable.
Most students were done within 15 minutes.
The next day, my students looked at their assessment and decided how to set a goal for their test.They used a simple Google Form that I created in Google Docs and shared with them. I created this to help them think about what they did well and what they need to work on before the final exam. It helps them be accountable to themselves. This particular group needs support in work ethic and striving for excellence. That accountability is what I believe will turn the table into a positive direction toward mastery of standards as a whole. I use these types of evaluations with every quiz and test I do. As the year progresses, they look forward to being able to talk about their growth.
When all the surveys were done, I evaluated how they perceive themselves as learners and examine how they understand their strengths and weaknesses. I will use this tool to help me keep track on a separate sheet. It makes it easier for RTI planning.My mindset for CCSS is not about grades as much as it is about mastery. I don't simply move a child on if he fails an assessment. Every child has the right to master the standard and I believe I have to be committed to make sure that happens. Rigorous? Demanding? Yes. This is what it is about.