I like to have students take assessments with my sub because testing days don't require a lot of teaching. This quiz is checking that the students are understanding how to add integers. Some students may be modeling with number lines or symbols while others may be comfortable solving them mentally after having learned patterns. When I get back I will be looking for some common mistakes which are finding the difference when integers with the same sign are being added or adding the integers when positives are being added to negatives.
The homework asks students to compare and contrast a subtraction problem and it's equivalent addition problem so they can begin to recognize the pattern. The homework relates the problems to the context of hot and cold cubes learned in earlier lessons (Mathmaster Chef series). The context helps them model the problem mathematically and helps them to recognize the relationships between the operations and use them to find a pattern. (mp7)
The warm up integer addition equations asks students to fill in blanks with the missing addend to make addition problems true. When I have a sub I also provide them with an answer document for the warm up integer addition equations answers. I show two different models for representing the equations. I show the number line with a verbal explanation as well as the plus (+) and minus (-) symbols with a verbal explanation. These representations and explanations help model the type of thinking students need to do when they are making sense of the problems. Asking them to find the missing addend instead of the sum forces them to think about the relationships between the integers that we have been exploring in previous lessons. (Which way do we go?, The Three Little Bears, How do you know?, Secret Number sub plan)It is important for them to understand these relationships in order to recognize the patterns that help them solve the problems. I do not want them rushing through the addition quiz using their prior knowledge about positive number addition, because the relationships are more complex.
After going over the warm up students may use the remaining classtime to complete the Integer addition quiz and work on the homework patterns in subtraction. When students are finished with the quiz they turn it over on their desks and the sub brings them their homework to begin. I copy a flower onto the back of the quiz so the teacher can easily see when someone is ready for homework.
The homework is two pages. One side asks them to solve pairs of problems (one subtraction and the equivalent addition). They are asked to fill out sentence frames using the hot and cold cube context from earlier lessons (Mathmaster Chef series) and use a number line to model the problem. I use this context because it helps students make sense of integer operations and understand the relationships between integers and operations. It is important for them to use context and modeling because the relationships & patterns in integer operations are different and sometimes contrary to students prior knowledge of positive number operations. If students can first make sense within this context they can understand why the shortcuts we use work, so when they forget them they have something to fall back on and figure it out.
On the second page of the homework are two pairs of equivalent problems already solved correctly with their hot and cold cube context and their completed number lines. Students are asked to look for any similarities and differences. I am hoping they will notice that the solutions and the number lines are the same. I am also hoping they notice that one is subtracting and the other is adding the opposite.