As we continue our journey through teaching fractions, it’s time to add and subtract. Again, modeling is key to helping students understand and explain the process of adding and subtracting fractions. The table below shows the expectations for adding and subtracting fractions in 4th and 5th grade.
- Understand adding and subtracting fractions as joining and separating parts of the same whole (4.NF.3a)
- Add and subtract fractions with like denominators (4.NF.3a)
- Decompose a fraction into a sum of fractions and record with an equation (4.NF.3b)
- Add and subtract mixed numbers with like denominators (4.NF.3c)
- Solve word problems by adding and subtracting fractions; use visuals to model (4.NF.3d)
- Add and subtract fractions with unlike denominators (including mixed numbers) by finding equivalent fractions (5.NF.1)
- solve word problems using addition and subtraction of fractions with like and unlike denominators referring to the same whole(5.NF.2)
- Use benchmark fractions and number sense of fractions to estimate mentally and decide if the answer is reasonable (5.NF.2).
Start simple: 1 orange plus 1 orange equals 2 oranges just as 1 third plus 1 third equals 2 thirds. This helps students relate the denominator to any other unit like oranges, miles, hours, etc. It can also help to realize that just as miles and feet can’t be simply added, neither can thirds and fourths. But, it can be done!!
Try using pattern blocks and number lines to add and subtract mixed numbers or improper fractions. Using pattern blocks helps students physically add up fractions or remove fractional parts when subtracting.
Here’s an example of how a number line could be used to add and subtract numbers larger than one whole. Number lines are great because they can easily keep going beyond one or even two wholes.
Adding and subtracting with different denominators takes an extra step. Egg cartons are a great way to show how fractions can be converted to a common denominator in order to add and subtract fractions since all cartons will have 12 eggs.
Even though word problems can sometimes be more challenging for students, having a real life context to work in can help students with really understanding why they’re learning about fractions. As students read and work to understand the problems presented, they can use some of the above models, or use grid paper to draw the problems to model their thinking.
Resources for Teaching Students to Add and Subtract Fractions