Lesson 13 of 19
Objective: SWBAT write and evaluate expressions to solve problems with rational numbers.
Do Now - Sprint
Students enter silently and find a “sprint” on their desks. This assessment includes 25 questions to be completed in 1.5 minutes. The first ten problems test students’ knowledge of benchmark fraction conversions and their decimal equivalents. The next 15 problems assess student speed with multiplication of positive and negative integers. Students who answer all problems correctly in 1.5 minutes or less earn 3 Achievement Points for their cards. All answers are reviewed as a class. I will state the first five answers and then call on students for the next 20.
Fluency is an important aspect to the new Common Core curriculum and it is important to practice with assignments like this to improve flexibility and efficiency with number operations. This does not mean that I expect all students to be able to perform tasks like this in the prescribed amount of time. I make sure to let students know this before reviewing the answers. While the speed with which these problems are completed should increase over time, "fast" doesn't necessarily make you "better". Accuracy is more important than speed.
Students are instructed to get their homework out and enter answers into clickers. Students who finish early will display their work for questions 2, 7 and 9. I will review these questions with the class paying special attentions to #7 and 9. These questions could be solved in different ways and I want to focus on the use of the commutative property to simplify the solution process. I will be scaffolding up to this idea by asking students to share the different ways they solve this problem and then asking other students which property students are using to move numbers around in the expression. Reviewing these topics also sets up the lesson in a way that shows the usefulness of showing work with the use of expressions. Use of the commutative and associative properties is also use of MP7 as we make use of the structure of a problem to reconstruct it using these properties. I will have extra vocabulary cards for associative and commutative property (these were given out at the beginning of the summer as well)
A persistent problem that is leading to multiple wrong answers on multiple students’ work in the way in which it is being organized. Many students are still using vertical arithmetic to solve complex multi-step problems. Today we will discuss how to use expressions to help us organize the work better.
The introduction to the task asks students to copy the definition for “expression” off the chalk board.
a mathematical expression that has a combination of numbers and at least one operation.
Students are then asked to turn to their neighbor and evaluate the work shown by two “sample” students. Student A uses expressions to neatly organize the work and solve step by step, whereas student B uses vertical arithmetic to arrive at a different answer. We will share out what was discussed for 2-3 minutes as a whole class. Student A’s work is neatly organized and numbers that she is not yet ready to use continue to get re-written in each step. This ensures that students do not continue to make the most common mistakes made in 7th grade: dropping of negatives, dropping entire values/numbers, and getting confused about the operations and the rules.
Next, students are asked to clear their desks of everything except for the task paper and a pencil. Each student is provided with a white board and marker. We will take the next ten minutes to complete the first 5 skill problems in the second page of the task on our white boards. By showing the work on the white boards I will be able to verify that students are understanding how to use expressions and simplifying step by step to improve mastery on these types of problems. Often, mistakes such as not following the order of operations and calculation errors with fractions and decimals will present themselves, making this an ideal time to remediate.
The procedures for this task goes like this:
- Students are asked to complete and indicated problem on their white board as i walk around
- While walking around the room I can provide some guidance through questioning and reminders to review sections of past notes. I am looking not only for correct answers, but correct procedures as well. Are students including the correct sign? are they multiplying straight across? are they reducing fractions appropriately? I may also need to remind some students that i need them to write bigger (or smaller) to make the work legible. The best aspect of whiteboards is that they make the process of erasing ans starting over less frustrating and even fun!
- Once students have had at least 3 minutes to work I go back to the front of the room and ask them all to hold up their boards. I am looking for the incorrect answers so that I know whom I should visit in the next problem. I am also looking for a correct answer with correct, legible work. All students will be asked to look at this solution and I will point out the best aspects/strategies in the solution.
I like the whiteboards being shown at the same time because it gives me immediate feedback about smaller groups of students struggling, but it also alerts me when there is a larger problem with a skill or concept. If I have very few students with a right answer/procedure on boards, I iwll be able to see this right away and review the problem on the board.
After 10 minutes of working on white boards, students will be asked to continue working independently and silently for ten additional minutes. Depending on the amount of work completed, students will take the last ten minutes to partner up in groups of three to complete the remainder of the task.
Students will use journals to explain in words how they used the associative property to solve #7. They will also be asked to explain the difference between the two properties we have been reviewing, commutative and associative.
At the end students will receive their homework and pack up for the next class.