In a perfect world, educational research would be readily available to teachers. Teachers would have time to read it and could then apply it to practice. Sounds nice, doesn't it? What if we told you that we synthesized the research, identified some key pedagogical and content ideas, and curated lessons that draw on those ideas? (You're welcome.)
And now, onto content.
KEY IDEA #1
In Grades 3 & 4, start by building conceptual understanding of the three types of fractions: parts of a whole, set, and line. Explore and experiment using a variety of representations. All the while, be extremely clear about what the "whole" is. LESSONS HOME/FAMILY ACTIVITIES |
KEY IDEA #2
Shift to a mathematical explanation of fractions. This hinges on students understanding that fractions are numbers. In contrast to whole numbers, the bigger the denominator, the smaller the piece. Number lines are an important complement to more concrete exploration. LESSONS |
KEY IDEA #3
Draw on a deep understanding of denominators to compare fractions and introduce equivalence. Comparing to landmark fractions helps "unlock the number system." Using a number line shows that equivalent fractions do not change in value - they stay put on that number line - despite changing the numerator and denominator. LESSONS |
KEY IDEA #4
Build on your students' preexisting knowledge of addition and subtraction of whole numbers. Start with addition; adding whole numbers (Fig. 1) and adding fractions (Fig. 2-4) are essentially just ways of combining things. Here again, a number line model is an effective visual representation in addition to concrete representations. After your students understand fraction addition, introduce mixed numbers (Fig. 5) and improper fractions (Fig. 6), both of which can be taught using the tenets of fraction addition. Subtraction can be taught using the same number line model that was used to teach addition (Fig. 7). LESSONS |
KEY IDEA #5
Teach multiplication and division using sequential steps, again building on computation of whole numbers: 1. Compute with whole numbers 2. Change 1 to a fraction 3. Swap 4. Change both to fractions Embed the computation in story problems, using manipulatives and drawings to build conceptual understanding.Like addition, multiplication of fractions is like multiplication of whole numbers. Division is simply repeated subtraction. |
KEY IDEA #6
Etc... |
Math Pedagogical Strategies
In addition to the videos embedded in the Lesson Plans (to demonstrate how the lesson can be executed in the classroom), here, we provide videos of teaching demonstrating strong practices that can be used across objectives and topics.
Check out this video of a 4th/5th grade math lesson. Notice how students have deep, mathematical conversations with partners and how the teacher pushes their thinking. (Source: Tim Bedley, rockinthestandards.com)
Check out this video of a 4th/5th grade math lesson. Notice how students have deep, mathematical conversations with partners and how the teacher pushes their thinking. (Source: Tim Bedley, rockinthestandards.com)
In this next video, notice how the teacher sets the students up with a complex, authentic problem and prepares them to engage each other in determining which of four models/solutions accurately depict the story problem that has been posed. (Source: Becky Pittard, teachingchannel.org)