Using his strong foundation of number relationships and simple operations, Jimmy will have an easy time building upon that foundation with multiplication and division, fractions and decimal places in 3rd – 5th grade. It is beneficial to encourage Jimmy to think of multiplication as quantity in Groups; division as the separation of the whole into Groups; and that a fraction is another way to express a division problem. That concept will naturally allow him to find patterns in multiplication and division facts and provide strategies to find answers, instead of learning them only by rote memorization. Fractions and rational numbers also come more naturally with this conceptual foundation of factors and multiples.
At 11 years old, Jimmy’s brain has twice as many synapses as an adult brain, which makes it the ideal time to ensure strong mathematical hardwiring (SECPTAN). In addition to brain development, this is a crucial social development period for Jimmy, as peer pressures and learned attitudes can easily affect his affinity for learning. He might decide or be told that he is “bad” at math and lose the enthusiasm he had in early elementary school. Providing opportunities to succeed is crucial, and supporting the idea that math isn’t about speed- it’s about a thought process- will help Jimmy maintain his confidence to learn. Reinforcing the importance of math in Jimmy’s daily life will help keep his learning active. He will be more excited about it if he makes the connection that we use multiplication, division, fractions and decimals every day when we figure out things like how to divide up candy or how many Groups of kids will ride the Ferris Wheel before it’s our turn. Jimmy’s attention span is increasing rapidly, allowing for more complex thought and multi-step equations and word problems. For Jimmy’s classmates who have difficulty with attention span, it helps if they can visualize and express each step in a systematic way to help with comprehension. Mnemonic devices can be useful, like using the phrase “Dirty Monkeys Smell Bad” to help students understand the steps of a division algorithm (divide, multiply, subtract, bring down). It often helps for them to say each step as they are calculating. At the end of 5th grade, Jimmy should be able to solve these number sense problems: 1. Half of a school auditorium is needed to seat 3 equal-sized fifth grade classes. Make a visual fraction model to represent the whole auditorium when each class is seated in separate sections. Write an expression and solve to determine what fractional part of the auditorium a single fifth grade class will need. 2. How many times greater is the value of the digit 5 in 583,607 than the value of the digit 5 in 362,501?