As students enter they work on the Warmup assessment and number line on the screen to prepare for their assessment of simplifying and factoring variable expressions using distributive property and like terms. The warmup is designed to review several elements that prove tricky for students at all levels. The first problem: 4(2m + c + 3) is meant to remind students not to combine variable terms with different variables or variable terms with constant numbers, to distribute the multiplication to all terms in the parentheses, and to put the terms in alpha order. Because this is an assessment, I don't expect students to make the first two mistakes, but I do expect some to forget the correct order.
The second and third problems: 3 + 2(5 + 2x) and 3(2x + 3) - 4 are meant to remind students to always follow the correct order of operations and complete the multiplication before doing any addition or subtraction outside the parentheses. Since this is the assessment I don't expect to see anyone try to combine the terms inside the parentheses. But I do expect more students to make a mistake on the first one and add first, so I want to watch out for this one. If I see anyone with terms that are way too big, this is what I suspect they did. They are more likely to make this mistake, because often they still don't take the time to make sense of what's happening in the problem before they just jump in.
The mistakes I expect to see with the factoring problem 16x + 12 are to just give an answer of 4 and not show the equivalent expression, since the directions just read "factor out the greatest common factor" or to put 4(16x + 12) and not actually factoring the 4 OUT. When I see this I ask students to double check that when they do the distribution it really is equal to 16x + 12...."will 4 times 16x gives us 16x?", etc.
The last problem sets them up for their homework. It asks them to fill in the blanks on a number line with positive and negative numbers. They have recently completed a problem called "consecutive sums" in which they had to find the types of number that could not be made by adding positive consecutive whole numbers. After completing it, students had questions about the number 1, the powers of 2, and what would happen if we didn't have to use positive numbers. Tonight's homework is the same problem, but it allows them to use numbers that aren't positive. The number line will help them recognize what "consecutive" looks like with negative numbers.
This is a Simplifying test of students ability to distribute multiplication over addition and subtraction and to factor out the greatest common factor from a variable expression. It also assesses their knowledge of like terms and order of operations.
I don't have a time limit on the assessment. If students need more time I will give it back to them tomorrow. When students finish their test I ask them to turn it over on their desk and I bring them their homework consecutive sums negative to work on for the remainder of class. To make it easier for me to see when they turn it over I copy a big flower on the back.
If students have trouble with the homework I ask them to copy the numberline that they made in their warmup and have them start with consecutive numbers from the numberline. By giving them this assignment before giving any instruction on adding negative numbers it will indicate how much they already know or remember. By the time we finish this assignment in several days they will have discovered that adding opposites equals zero and, using the identity property of addition and making pairs of opposites they can make any target number by adding consecutive numbers.
When I give students their tests back I don't put a grade on it, I just mark problems wrong. I have noticed that when I put the grade at the top, even when I allow test corrections, students just look at the grade and don't look at their mistakes. If I don't put a score on it they are more likely to look at what they did wrong and learn from it. Many of the mistakes that students can make on the Simplifying test common errors are going to be caught by them or by their math family group members. I often see students explaining and I hear a lot of ahas after a test.
I provide any help or answer any questions, but it is really the students that need intensive intervention that I follow up with.