Welcome to Week 2 of the teaching fractions series. Last week, we talked about basic meanings, and a little bit about fraction models. I 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 classes. Then, we’ll look at how to include fraction models in our teaching.
Fractions in Grades 1-4
1st Grade Math:
- halves, fourths, quarters, half of, fourth of, and quarter of
2nd Grade Math:
- Students partition rectangles into rows and columns of ‘same-size square’ and count to find the total number
- Students again partition circles and rectangles into 2 and 4 parts, but add on partitioning into 3 parts. They continue to use halves, half of, etc. and add on thirds and a third of.
- Students should be looking at wholes and identifying those as two halves, three thirds, and four-fourths.
In 3rd grade math, there’s a lot more going on!
- Students partition shapes into parts with equal areas and identify each part as a unit fraction (1/3,1/4,1/2, etc.)
- Students begin to develop an understanding of fractions as numbers, representing fractions on a number line, and “understanding two fractions as equivalent if they’re the same size or the same point on a number line.”
- Students recognize and generate simple equivalent fractions and should also explain why the fractions are equivalent.
- Students express whole numbers as fractions, like 5/1 = 5
- Students compare two fractions with the same numerator or the same denominator ‘by reasoning about their size.
In 4th grade math:
Students should be doing SO many of the fraction things. I’m not going to list out each skill, but the general goals of fractions in 4th grade Common Core are:
- extend understanding of fraction equivalence and ordering
- comparing fractions with different numerators and denominators by using common denominators or benchmarks
- build fractions from unit fractions (includes understanding addition and subtraction as joining and separating parts, as well as decomposing fractions into sums of fractions)
- add and subtract mixed #s with like denominators (replacing each mixed number with an equivalent fraction)
- solve word problems with addition and subtraction
- multiply fraction by a whole number and understand that a/b (like 5/4) is a multiple of 1/b (¼)
- solve word problems involving the multiplication of a fraction by a whole number
- understand decimal notation for fractions, and compare decimal fractions
I think it’s important to note that ‘using visual models’ is included in numerous places in these standards.
Fractions in 5th Grade Math (and beyond)
- Some students aren’t developmentally ready for all the fraction concepts
- Some classes may not have gotten as far in the curriculum as they needed to and may never have discussed certain fraction topics
- OR they did discuss the fraction topics, but very quickly or maybe with shortcuts, because there just wasn’t enough time
So that’s all well and good….students are supposed to have done all of this, should be proficient at these fraction skills, and should be ready to apply them and go deeper at the next grade level.
But what are math teachers at 5th, 6th, or higher grade levels supposed to do when this isn’t the case, and their math curriculum builds on that prior fraction knowledge? The ‘time’ issue continues to be an issue. Where does reteaching fit into the curriculum? (A question for many math concepts, but we’ll stick to fractions here!)
Teaching Fraction Models in Middle School
Let’s look at how using models might be able to help. Based on the standards, students should have been using various models before hitting 5th grade – area models, length models, set models, and number lines. Continuing to use these fraction models will only help students connect the concepts with the processes.
One way to help students bridge some of the fraction gaps (or just refresh their memories) is to incorporate these visual models as much as possible.
When teaching a new fraction concept (or briefly reviewing concepts from previous years), bring in the fraction models.
On their models, students can add partitions to show both fractions as sixths, encouraging the continued development of equivalent fractions.
The addition and subtraction of fractional parts is visual for middle school students when they use fraction models.
This combination of process and modeling helps students connect the process with the meaning of the operations or simply finding equivalent fractions.
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Other Fraction Models
Fraction Toolkit
Do you need a few tools to help your students master the fraction basics? I’ve got a ‘Fraction Toolkit’ for you!You can grab the Fraction Toolkit and learn how to use it for your classroom needs.
