As students progress in their math program, they will be presented with more complicated equations and given opportunities to decompose numbers. The basic fluency sense of using ten as a benchmark will continue to follow the students from basic computation to difficult. When this program is followed from the beginning of kindergarten and carried through continuously, the strategies build with purpose. Students are connecting those lower level skills as they grow and they become more difficult. What are benchmark numbers? Benchmark numbers are the numbers the students want to calculate ways to get to make mental math a smooth process. For example, if a student has to add 16+4, they make think of making a number bond out of 16 and decompose the number into 10 and 6. Then add the 6+4 to get 10. Then add 10+10 which equals 20. At first this is taught in the form of making a number bond. Later on, students begin to see this process mentally and phase out that step. I like to tell my students that like a park bench, benchmark numbers are a nice place to stop and rest before moving on in the problem. Another way benchmark numbers are helpful is when completing patterns. If a student has to show a way to count from 76 to 140 using tens and ones, benchmark numbers gives them the process they will need to explain their thinking. For example, a student may say I counted by ones to get to the nearest benchmark number after 76 which is 80. Then it was easy to count by tens from 80 to get to 140. We want students to count in the most productive way. Younger students are tempted to count by ones as long as they can. When they see they can mix the use of counting by ones and tens, they can make it to the benchmark number quicker.
When moving into a visual activity, students may look at groups of stars. Then they will ring together the amount of tens and ones. They will specify there are ___tens and there are ___ ones then ____stars in all. When students are using the abstract form of ten as a benchmark number. They will calculate equations. They may even move numbers to make a ten and give themselves a nice number to calculate. For example, 23+12. They can say, “If I look at this equation as 25+10, I can add that fast because ten is a nice number.” This process becomes fluent and students begin to process these calculations with minimal effort. I find this the most rewarding aspect of Eureka Math. The way my students explain their thinking to me using this process is amazing. Sometimes, I have already thought through my entire lesson. I have a planned strategy for them to use, and they begin to evolve it even further and explain different ways to decomposing the numbers to me. I have honest reactions of, “I didn’t think of it this way, but yes that is right too!” The versatility the students are given and the freedom to think on there is own is what makes this way of teaching so strong and the students’ learning so productive for not only their days in school, but beyond the classroom. Make It Fun! We always to draw students in a way that hooks them. Here are some fun activities you can use in your classroom as centers or partner work while teaching students use tens as a benchmark numbers:
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