Students enter silently and find another “sprint” on their desks. This assessment includes 25 questions to be completed in 1.5 minutes. All 25 questions require students to memorize benchmark fractions’ decimal equivalent. At the end of one minute, students who raise their hand to indicate they’re finished will have their paper stamped and collected for grading. Students who answer all problems correctly earn a homework pass. All answers are reviewed as a class. I will state the first five answers and then call on students for the next 20. If a student does not know the answer I will have them calculate it on their paper with long division while I have other students call out the answers in the rest of that row. Then I will come back to the student who calculated the answer to ask again. Students who are getting all answers correct can convert on more rigorous fractions posted in the room on chart paper (i.e. 19/23).
Homework is entered into clickers and answers are reviewed for problems mastered by less than 50% of the class. Many students are still struggling with these operations, so a brief discussion of “grit” is led. Students who see better scores in their work with these operations from one day to the next share strategies that helped them get better. Students who have questions about the “most confusing parts of these types of problems get to ask and offer example of problems they would like to see solved. I call on other students to go up to the board and show the solution. This part should take no more than 4 minutes.
Next, students receive a copy of slides 3 and 4 from the power point. These are the “rules for adding and subtracting rational numbers”. They include examples of problems with the use of variables to represent the different types of addition and subtraction variations. Students are also provided a sheet protector to house these rules in order to easily refer back to the rules. We then complete more practice problems as a class from the power point presentation. We review the first 2-3 problems together and I ask students to pay close attention to the strategy used to solve:
For example, the first slide includes the problem 4 – (–20). To solve this problem we look at the subtraction slide, 3rd bullet point, for the problem that “looks like this x – (–y)”, the rule states “use the additive inverse to simplify double negatives”. This means we add the opposite of twenty and the problem becomes 4 + 20 which equals 24.
After reviewing three problems as a class students are asked to work with partners for each consecutive slide by using the same step by step strategy modeled. By reviewing the notes, or the rules, students are making use of their notes and MP8 because they are looking for and applying regularity in repeated reasoning.
The most difficult problems included in the ppt include fractions with unlike denominators and a diversity of signs and placement. For example, slides 10 and 14 are difficult for students because they are first thrown off by the way the numbers are placed (i.e. smaller in front of larger when subtracting).
One strategy I give students is to first ignore the signs and make the fractions "speak the same language" (make the denominators alike). Once the denominators are alike, the numerators can be treated as integers and were back to number line models and blue/red chip models.
Students are given 21 more skill problems to complete. They must work independently for ten minutes, practicing the applications of the rules to their problems. After 10 minutes have passed, they are asked to form groups of 4-5 with students in the 1st and 2nd rows grouping together and the 3rd and 4th rows doing the same. Students will also be required to enter all answers into clickers.
As I walk around I will make sure to listen in one the types of questions students are asking each other. I will make sure that answers are not the only pieces of information being shared, but also justifications of the answer with the use of the language in the rules (i.e. finding differences, calculating absolute values).
Clicker assessment is stopped and least mastered questions are reviewed, with the focus on the strategy of asking the same series of questions:
Homework is distributed and students are advised that it will be graded.