Math Misconceptions
What misconception is this?
The student might skip numbers or go out of order saying "one, two, four, nine, three, five".
The child does not know the counting sequence
What is the strategy to support students who do not count in sequence?
Read counting books
Use an activity involving correct and incorrect ways of counting for students to identify the mistakes
Match the written work with the number
Define Commutative Property
When you add two numbers in any order you will get the same answers
Give an example of a fraction equivalent to 1
ex: 5/5
Which is bigger?
3 inches or 6 centimeters
3 inches
What Misconception is this?
24 - 7
Student subtracts 4 - 7 as 7 - 4 and gets an answer of 23
Student overgeneralizes the Commutative Property of addition and uses it in subtraction
How would you address the misconception of the student choosing the wrong operation from a word problem?
Cover up the numbers in the word problem and have the students read the problem.
Have concrete materials available to model the problem
Define Distributive Property and give example
When you multiply two numbers you can split one into two parts (7 can be 5 + 2) multiply each part by the other number and then add them together.
Ex: a X (b + c) = a X b + a X c
Write the whole number 25 as a fraction
25/1
Name 3 equivalent fractions to 7/8
14/16, 70/80, 28/32
What misconception is this?
Student is not able to think of 14 - 9 as "What plus 9 equals 14?" or 36/4 as "How many groups of 4 are in 36?"
Students do not recognize inverse realationships
How would you address the misconception students reverse the digits when writing two-digit numbers?
ex: writes 53 as 35
Use base ten blocks to display number
What is perimeter of a 2D shape?
The perimeter is the distance around a shape
8/12 = n/6 n=?
n=4
write the decimal, % and fraction to the following
50%
2/3
.363
.5, 1/2
.667, 66.7%
363/1000. 36.6%
What misconception is this?
70 - 23 = 53
Student explains 0 from 3 equals 3, and 2 from 7 equals 5. The answer is 53
When subtracting two digit numbers, student always subtracts the smaller number from the larger number rather then regrouping.
How would you address the misconception?
Students always put the word "and" in a number when they read it aloud.
ex: 1,200
one thousand and two hundred
Students must practice reading numbers without using the word "and". The only time the word "and " is used is to represent a decimal.
Define Equivalent Fractions
Fractions which have the same value but may appear in different fraction form using different digits.
5 divided by 2/3 =
7.5
What is the circumference of a circle?
Draw a model to illustrate.
What misconception is this?
4005 X 9 = 3645
When multiplying students ignore the internal zeros
How would you address this misconception?
Multiplication makes "bigger" numbers and division makes "smaller" numbers
Concrete materials to model problems
Students are overgeneralizing whole numbers to fraction/decimal concepts. Need to address basic understanding.
Define Volume
The amount of units fitting inside a 3D shape
4.5 + 1/4 =
4.75
Name the 4 Levels of Knowing in Math
1. Intuitive
2. Concrete models/visuals
3. Abstract Thinking/Algorithms
4. Application/ Real World