In planning meetings, we always hear our peers talking about how to differentiate for the varying levels of students within one classroom. However, the majority of the time, teachers are discussing how to help the struggling students. Maybe the students are below reading level, therefore, they have difficulty reading the word problem in math. Or perhaps the student struggles to retain the information and cannot learn the many steps to complete the long division problem. These students are the ones most people focus on in planning meetings; working to get them to grade level. What about the students who are above level, and need more challenging activities? Most times, these students are the ones who get lost in the shuffle of differentiation.
The typical solution for these students who are above grade level is to continue with the standards, then pull standards to teach from the next grade level. However, this is not the best way to meet these students where they are and push their understanding of new material. There are several ways to extend their learning at a deeper level. We should focus on making sure they have a firm understanding of the current standards from all angles.
Multiple Paths to One Correct Answer:
There are multiple ways of coming to an answer in almost every type of math problem. Students can use various strategies in order to get the correct answer. This is what I love about math - one correct answer, no interpretation! Those students who are above level, can be challenged to learn how to solve the problems in multiple ways. A student can be challenged to complete their multiplication or long division problems in more than one way. Once they are really good at partial quotients, they can move onto long division. Once they are successful at Box and Cluster for multiplication, they can practice the standard algorithm. Once students understand that to find the perimeter of rectangles, they add up all the sides, they can then work on the formula 2Lx2W to find the same answer, which is considered more advanced. When students get the correct answer, can they also explain in word form how they got the answer? In order to have a strong understanding of the skill, they must be able to justify their process and final answer.
Once these advanced students have met the standards and practiced more ways to get their correct answer, they can explore a topic they are interested in. Some math related focuses could be logic puzzles, math patterns, or learning math strategies from other countries. These are all extension topics for the advanced students that fall outside of the typical required standards. I love using code breakers to make my students think! My code breakers are based on multiplication facts, but students have to use images to crack the code, which is the answer to themed jokes.
Real World Applications:
When I start planning my units, I always think about how the skill is used in real life. I don't ever want my students thinking,"I will never use this". I try to make connections so students understand why the skill is important. Once my advanced students are ready for an extension, this is the perfect time to push them to learn about future careers. For example, during our area and perimeter unit, their extension could be learning about the professions that use area and perimeter daily to do their jobs. What careers, jobs, or trades use these formulas? What type of numbers do they work with (small numbers, large numbers, fractions, decimals, etc.)? What are the formulas used for? They could then create a product to show how it is used. If they studied welding during the fraction unit, they might make a diagram of different measurements to show what would need to be cut and welded. If they studied architecture during the area and perimeter unit, they may design a house using realistic measurements for each room. These extensions give students a real world view of how math is used every day.