Students enter silently and find another Sprint on their desks. This assessment includes 20 questions to be completed in 1 minute. All 20 questions require students to memorize benchmark fractions’ decimal equivalent. it is important to memorize these benchmarks to aid in more complex rational number operations. Knowing these benchmarks by memory can help students compare values to better determine their relevant magnitude in any given word problem. These facts can be used to compare rational numbers, estimate or approximate values in problems.
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.
Students then review the answers to the HW sprint questions with their neighbors.
Three students are asked to read the steps for problems solving.
1) Read the problem
2) Draw a model
3) Use the model to write an equation/expression
We complete #2 and #4 together and then students are asked to work with partners for 10 minutes. After this time, students work independently to complete 11 problems and enter their answers into their clickers. I will be walking around the room with a white board helping students model the word problems.
Many problems' models will include a number line and an interpretation of the context of the situation. This is why I am choosing to review #2 and #4. The idea of "relative" height or speed comes up in several problems as well. For #2, we will be drawing a vertical number line where we interpret 0 as the location of "the ground". Students are guided to think about the meaning of the question "Which ant is closer to ground level?" by asking "Are we looking for a number closer to zero or further from 0"? Problem #4 refers to the relative position of runners behind the first place winner.This is a multi-step complex problem. It asks students to understand that they must order the rational numbers from least to greatest, it requires knowledge of fraction/decimal conversion, and the most difficult concept, the idea of "relation" to the first place winner. On a number line model, the first place winner is graphed at zero. All other runners are graphed in appropriate order so that I can show students the location of the second place and 5th place winner. Students will be guided to consider the question "Who finished in second place?" and figure out what they need to do with all the numbers in order to find the second place winner. Since the rational numbers need to be ordered from least to greatest, students are then asked to interpret "2nd place" on that horizontal number line. (See images attached in this lesson) Reviewing these examples will allow students to complete questions like #11, which is one of the most rigorous. This question asks students to consider relative speed (like #4, relative placement). Relative speed is written as a rational number that is used to compare different speeds to the fastest. Thus, in order to get the second fastest speed, students need to deduce that they are looking for the largest rational number in the list (-0.15). By subtracting the fastest speed minus this rational number, one can obtain the second fastest speed. By applying their understanding of rational numbers' placement on the number line for this problem (and for most in this task) students are using MP4 as they apply they math they know to interpret and solve word problems.
Assessment is stopped. Lowest scored questions are reviewed. Model drawing is reviewed for each of these problems. Homework is distributed; it is a skill drill worksheet to help students continue to practice the basic skill of adding and subtracting rational numbers.
The three lowest scored questions in the classwork were consistently #1, #6, and #7. Question #1 brought down students who continue to struggle with understanding of fractions, this group makes up about a third of the grade. Question #6 was most confusing to students who struggle with reading comprehension, while question #7 was challenging in terms of the vocabulary (overall). I believe that what my students need most are strategies for comprehending what is happening in the problem. I see many of them speed reading (if reading at all) through the word problems, hardly checking to see if they understood the story line, then feeling frustration when unsure how to solve.
One strategy I use is to have students read the problem at least three times, stopping each time to ask themselves if they understood the story line, or what happened. Visualizing is a big part of our problem solving strategies as bar models and number lines have become so central to this new curriculum. Finally, a last strategy I ask them to use is talking to a neighbor and summarizing or discussing (through questions) the word problem.