## Number One:

## If you want to build proficiency with subtraction at any grade, you must not be afraid to move things in your head.

Start by moving things in real time and discuss the affects of the move. So here is a ChunkitZ puzzle. I see 3 and 2. That’s 5.

How do I know this is still 5? I turned the 2, (quarter turn left) flipped it over (reflected) and slid it down to match the left hand side.

I see 8 = 8 because I see 6 + 2 in each of them.I turned the 6 (one quarter turn to the left). Then I slid the dot on the far left side of the middle row down below and lined up with the middle bottom dot. I slid the dot on the far right side of the middle row up. It is above and lined up with the middle top dot. It is still 6 and 2.

## NUMBER TWO: Subtraction is an action that emerges when you want to make things equal or maintain equality. These are not equal. One way to make them equal is to remove from one side.

IT IS CALLED SUBTRACTING not take away. first I did a quarter turn to the left. Then I removed one dot and pushed the other to the right. Yes, the action was a removing action but the mathematical term is subtract and the sign we use is a subtraction or minus sign. WHEN STUDENTS HAVE THE VOCABULARY, THEY CAN JOIN THE MATH COMMUNITY. Vocabulary is a part of community. You have to speak the language to join the club. we correct DA DA to become daddy or dad or even father but we leave take away??? I do not agree. You do not take away to solve every subtraction problem.

## Number 3: Addition and Subtraction are RELATED. Teach them together, first as a relationship.

If you can add, you can subtract. Since 1997, the Western Protocol for Mathematics and the Alberta Program of Studies for mathematics which emerged from it, has stated this as an outcome in mathematics. Students need to know and understand that addition and subtraction are related. In the 2004 revision, the statement think addition for subtraction was used as a strategy. HOWEVER, it is not just a strategy it is an actual property of our number system. The focus is relationships before equations. Understand the relationship, talk, describe explain the relationship. Then introduce the notation. Not the same day, but once they can explain…..

INVERSE OPERATIONS, is a critical understanding students need to be able to apply when they work with integers, rational numbers and algebra.

## Number 4: Subtraction is not just a “taking away”.

#### It is a comparison. Taking part of the whole away can reveal the answer but the comparison might be phrased as difference between. In that case you are looking at 2 lengths or heights, or weights or quantities and comparing them.

*My sunflower is 4 meters tall. My mom’s is 3 metres tall. How much taller is my mother’s sunflower. (You do not see taking a sunflower away in your head. You see the space between the sunflowers.)*

## B.E.R.C.S. cards and tasks were designed to prompt and promote visual spatial reasoning. They focus on the relationships that matter. They prompt communication, problem solving and critical thinking. Use them to support your Guided Math approach. Use them to open lessons as warm-ups or as the introduction to a lesson. Use them with small groups or individuals for added practice. Use them to differentiate so that every student builds his or her full potential.