We teach 5th grade fractions using a “Sandwich” strategy.
- August/early September: We introduce the visual method to add and subtract fractions. (See our blog entries from Aug. and Sept.)
- October/ November: We go on to the next two units (1: patterns and 2: Multiplication/Division). During that time, though, each homework assignment and each quiz has ONE fraction problem to solve pictorially. Students still have access to their Fraction Template (see below). Students who have mastered this skill do not complain about doing that one problem, but it greatly aids our visual/concrete thinkers. For these students, 2 or 3 weeks of drawing does not suffice.
- This repeated practice for a few weeks is what it takes for ALL our students to master the pictorial solving of fraction addition and subtraction. Then, in January, we can return to fractions and transfer their understanding to the abstract algorithm in a matter of a day or two.
- Here’s an example of a 5th grader who could NOT solve fraction problems in August — she did have a murky understanding of the algorithm, but it did not transfer to subtraction, to word problems, or to multiplication. Now, she can do it! She drew the 3 and 1/4. Then she crossed out 1 and 5/8, and counted up what was left over — voila, the answer! ( Quiz 5 , Level 1)
- Teaching this tool, this one visual strategy, means you don’t have to teach fractions again and again (!) in 6th and 7th grade (and beyond!). Students have something to fall back on. Visual memory is far more robust than algorithmic memory for most people.
What about the rest of Quiz 5? How are students doing with patterns?
Level 1: Student can draw/count up the first 5 figures of a series, but not yet derive the abstract concept of the pattern that is applicable to bigger numbers.
Level 2: Student can WRITE OUT the first 43 figures of a series, but not yet derive the abstract concept of the pattern that is applicable to bigger numbers.
Level 3: Student can see that the 43th figure would be (starting at figure 1) 42 new increments of 3, therefore 42 x 3. (From figure 1 to figure 43 is an addition of 42 stages, not 43. ) We did not teach this — it becomes noticeable to the child when their abstract skills have grown to that level.
Level 3: This student saw it differently — looks good to us! Can you follow their thinking