Solve word problems involving the addition and subtraction of fractions with unlike denominators. Recognize mistakes in adding unlike denominators. For example, \(2/5 + 1/2 \ne 3/7,\) because you can't simply add numerators and denominators.
Watch these Khan Academy videos:
Add and subtract fractions word problems by Khan Academy
Next, give your students these challenges:
- Cube Bricks and Daisy Chains by NRICH
How Many Triangles Do You See? Challenging Puzzle by MindYourDecisions: When providing the solution, give both the solution found in the video, and my more elegant solution, which is as follows: Draw the lines of symmetry, a horizontal line and a vertical line. Consider one quadrant, whichever one you like. There are 4 triangles that occur entirely in that quadrant. These 4 triangles will occur 4 times, because there are 4 quadrants. There are 2 triangles which are cut by the vertical line of symmetry, but not the horizontal. These 2 triangles will occur 2 times, because there are 2 halves. There are 6 triangles that are cut by both lines of symmetry, and thus occur only once. Hence, the total number of triangles is$$4 \cdot 4 + 2 \cdot 2 + 6 = 26$$
Conclude by leading this investigation:
Toothpick, Vampire and Domino Sequences
5.NF.A.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.