Thinking Skill: Infer
The 'Infer' thinking skill in Grade 6 Saxon Math Course 1 applies to fraction problems where finding a fractional part requires an intermediate inference step. When a problem asks for n/d of a total, students infer that finding 1/d first (by dividing by d) enables finding n/d (by multiplying the unit fraction by n). For example, if 2/3 of students ride the bus and there are 360 students, infer: 1/3 = 360 ÷ 3 = 120; then 2/3 = 2 × 120 = 240. This structured inference prevents guessing and builds systematic reasoning.
Key Concepts
Property When a problem asks for a fraction of a total, you must first find the size of one unit fraction. To find $\frac{n}{d}$ of a total, you must infer the first step is to divide the total by the denominator, $d$.
Examples For $\frac{2}{3}$ of 12 musicians, you divide by 3 to find that one 'third' is 4 musicians. For $\frac{3}{5}$ of 3.00 dollars, you divide by 5 to infer that one 'fifth' is 0.60 dollars. For $\frac{9}{10}$ of 100 percent, you divide by 10 to find that one 'tenth' is 10 percent.
Explanation Why divide first? Think of the denominator as a clue telling you how many equal shares a treasure is split into. By dividing the total by this number, you figure out the size of just one share. Once you know the value of one piece, you can easily calculate the value of any number of pieces, just like a detective solving a case!
Common Questions
What does 'infer' mean as a thinking skill in math?
To use given information to determine an unstated intermediate step needed to reach the solution.
2/3 of 360 students ride the bus. How many is that?
Infer: 1/3 of 360 = 360 ÷ 3 = 120. Then 2/3 = 2 × 120 = 240 students.
3/5 of 45 problems are completed. How many?
1/5 of 45 = 45 ÷ 5 = 9. Then 3/5 = 3 × 9 = 27 problems.
Why is the 'infer' step important?
It identifies the intermediate calculation (finding the unit fraction) that makes the multi-step problem solvable systematically.
How does the infer skill connect to proportional reasoning?
Finding a fractional part is proportional reasoning: identifying the unit rate (1/d of total) and scaling up by the numerator.