Challenge Allert!
This set does not contain any incorrect answers. However, due to common misconceptions, children may mistakenly evaluate these correct answers as incorrect. The gem of this set are the discussion questions, which will help children clarify their understanding of related concepts.
Examples of Correct Answers that Might be Perceived as Incorrect
Discussion Questions
Example 1
Questions to Ask
- What does the equal sign(=) mean? (the same value)
- Is the total of 3 and 2 equal to the total of 2 and 3? (Yes. If children are not sure, put three blocks/gold fish/m&ms in one hand and two in the other hand, and then swap hands, ask them whether the total stay the same after swaping hands)
- When you’re adding numbers together, does it matter what order you put them in? (No, you can add numbers in any order, and you’ll still get the same answer. The total of 1+2+3 is the same as the total of 3+2+1. Use manipulatives to demonstrate.)
Example 2
Questions to Ask
- What does the equal sign(=) mean? (the same value)
- When we add numbers together, does adding three numbers always result in a greater total than adding two numbers? (no)
- Can you give me an example when adding three numbers lead to a smaller total than when adding two number? (1+1+1 is smaller than 100+100. )
- Can the total of two numbers be equal to the total of three numbers?
- Without adding the two number on the left or adding the three numbers on the right, can you tell whether the value of the left side is the same as the value of the right side? (Yes, because 5+1 is 6, 5 and 5 are the same)
Common Misconceptions
- The equal sign (=) means “make”, which is an action.
- When children are given addition problems, like 3+3=, they are often asked, ‘What does 3 and 3 make?’ They then write down the answer to complete the equation, such as 3+3=6. This kind of experience can sometimes lead them to interpret the equal sign as a one-directional action of “making”.
- The equal sign (=) means the numbers on both sides have the same value. For example, 2 + 3 = 5 means that 2 plus 3 is the same as 5.
- You have to add the numbers in the order given.
- Because children tend to interpret the addition as a one-directional action of making, they see the numbers given as steps for this action–they need to start with the first number, followed by adding the second and third number.
- When you’re adding numbers together,
it doesn't matter what order you put them in. You can add numbers in any order, and you’ll still get the same answer. This math rule is call the commutative property of addition. - Knowing such rule is especially helpful for children to discover addition strategies that make their calculation easier. For example, if they are given question 3+55, when using the strategy of counting on–start from a number as the base number and then count on the second number to find the total, it is a lot easier to start with 55 and then count 3 more than to start with 3 and count 55 more.
- The more numbers you add, the bigger the total is.
- Because in children’s everyday experiences, they usually add more cookies, fruits, or toys to their collections. Every time they add more items, their collection gets bigger. So, they tend to think that when you add more numbers, the total becomes bigger.
- Adding more numbers doesn’t always make the total bigger. It depends on the numbers you’re adding. Sometimes, you can get the same total with fewer numbers, and sometimes you need more numbers to make it bigger.
Concepts Invovled
- The equal sign (=)
- Addition
- Decomposing of numbers
- Commutative property of addition
