Fraction Series, Week 3: Benchmarks and Estimation
In the fraction standards review part of last week’s fraction post, I briefly summarized the fraction skills addressed at different grade levels.
In 4th grade, we have “comparing fractions with different numerators and denominators by using common denominators or benchmarks.”
When we move to the 5th grade standards, we see benchmarking is also included in 5.NF.A.2:
Using Fraction Benchmarks
Using benchmarks to estimate is a powerful way to help students understand whether or not their answers make sense.
I'm not sure if your experience is the same as mine, but over the years, I've observed that this understanding of whether or not answers make sense is definitely an area of weakness for students (not just in the area of fractions).
So, if we can incorporate the reinforcement of benchmarks, estimating, and the understanding of 'reasonable' it will be a huge benefit to our middle school students.
Let’s look at the 4th grade concept of using benchmarks to compare fractions.
When students are asked to compare fractions like 5/8 and 2/5, for example, the standard would like them to be able to look at 5/8 and think:
This is great logic. I have found, however, that some students don’t know how to find half of a number and even if they do know, they have trouble with half of an odd number. Have you found this too? That may be something for another post!
When it comes to using benchmarks in 5th and 6th grades and beyond, we might not be using them as much to teach comparing fractions; but we can teach using benchmarks (and finding half) in the context of estimating answers for adding and subtracting fractions (and eventually for multiplying and dividing).
Reviewing the Standards and Using Fraction Models
Welcome to Week 2 of the fraction basics series. Last week, we talked about basic meanings, a little bit about fraction models, and suggested a couple ways to work fraction basics into everyday instruction.
This week we’ll take a look at the progression of fraction skills through the grades before our students reach us in upper elementary and middle school math class. And then we’ll look at models:-)
Fractions in Grades 1-4
As upper elementary and middle school math teachers, we know our students have had fraction instruction – what fractions are, identifying fractions of shapes, finding equivalent fractions, comparing fractions, and some fraction operations; but we may not know exactly what students did in which grades.
So, for a 'quick' overview (based on the Common Core Standards), in the earlier grades (1st – 4th ) students should be learning/mastering the following:
1st Grade Math:
I think it's important to note that ‘using visual models’ is included in numerous places in these standards.
End of Year Activities for Upper Elementary and Middle School
Are you approaching the end of the school year?
Does it feel like the school year flew by and it's already the end of the school year? Or did it seem slow in coming this year?
Regardless of how quickly or slowly your school year went, the end of the year is a great time for students to look back and reflect on the time they spent at this grade level.
If you're looking for a few activities for the end of the year, I have a few ideas for you:-)
End of School Year Activity #1
1) Students can write letters to themselves. You can have students self-address their envelopes, and then you can save them and mail them to students in August.
Kids are so excited to receive actual letters in the mail!
AND, addressing an envelope is great practice for a life skill that isn't used quite as often these days.
For most of the years we did this, many of my students had never addressed an envelope before.
Welcome to this blog series about teaching fractions in middle school!
For the next several weeks, we’ll be looking at various aspects of fractions: basic meanings, fraction models, finding equivalent fractions, comparing fractions, benchmarks and estimation.
As an upper elementary or middle school math teacher, you may find yourself needing to review some of these fraction concepts before you can move on to the fraction curriculum for your grade level.
When this is the case (needing to review fraction concepts that aren't part of your curriculum), there usually isn't much time to squeeze in extra instruction...it can be tough!
We realize that some of our middle school kids just don't 'get' fractions, but our time is limited. I've got a couple ideas at the end of the post for how to weave in some of the 'fraction basics' in middle school.
But first, for this week, we’ll start with some of the foundational fraction vocabulary terms.
Hey there! I'm Ellie - here to share math fun, best practices, and engaging, challenging, easy-prep activities ideas!