Breaking Down the Question Barrier

Children need to be exposed to the forms of mathematical thought as well as to the details. What is missing in most instruction is the timely unfolding of these basic forms of mathematical thought. The use of consistent, familiar forms clearly depicts the underlying structure and helps eliminate confusion and uncertainty.

 

Without the structure provided by the Question Forms, classroom instruction often disintegrates into the usual collection of details—facts, operations, and procedures—that have characterized unsuccessful mathematics education for decades. All students (“at–risk,” “at–level,” and “talented” alike) benefit from having new material in mathematics presented as reoccurring manifestations of the same set of basic ideas with which they have already become familiar.

Let’s start with questions in the “single-form” format. Each is a breakdown of the format of questions based on one single concept; this allows your student to lay down a base to build a foundation on.

Counting, Grouping, Intervals: 
Count from _____ to _____ by _____s 

     Count from 2 to 16 by 2s...from 1 to 15 backward by 2s.

Denomination and SAMEness:
 What is another name for _________? 

     Name 2 numbers that add–up to 15...to 25...to 75...to 100.

Subtraction and Addition:
 How far is it from _____ to _____?

     How far is it from 5 to 11?...from 13 to 20?

Order: 
_____ is greater than/less than/equal to _____ .

     Name 3 numbers that are between 7 and 10.

Multiplication:
 How much are _____ groups of _____ ? 

     If you see 8 eyes, how many people are there?...16 eyes?...100 eyes?

Division:
 How many _____ are there in _____?

     How much is 1 + 1?...2 + 2?...4 + 4?...8 + 8?...16 + 16?...(continue as far as you students can go mentally.)

Fractions and Fractional Parts:
 How much is _____ (fractional part) of _____? 

     Half of what number is 7?...is 1?...is 12?
How much is half of 8?...of 12?... of 18?... of 200?...of 1,000?

“The Whole is equal to the sum of its Parts”: _____ (whole) = _____ (part) + _____ (part) 

     A cook bought two bags of apples. One bag of apples weights 15 pounds and another weighs 10 pounds. How much is left after the cook uses 17 pounds of the apples for pies?

Percent: 
_____% of _____ is _____. 

     How much is 50% of 6?...of 20?

Ratio:
 _____ is what part of _____? 

     Is 7 half of 14, or is 7 twice as much as 14?

Change and Variation:
 As _____ gets bigger/smaller, _____ gets bigger/smaller. 

     Does it cost more to buy 5 apples or 10 apples? Why?

Proportion: 
_____ is to _____ as _____ is to _____ . 
     Does it cost more to buy 5 apples or 10 apples? Why?

- Larry Martinek