Subtraction

We are beginning work on subtraction.

Today’s Problem (Nov 4):

Today’s problem (and the important information the students pulled out of the question:

Most students used a traditional strategy to solve the problem:

Some students also checked their work with addition:

Some students gave excellent explanations of their work:

One group came up with a different way to solve the problem.  They focused on a connection with one of the addition strategies (Breakdown Jr.) and came up with this:

Consolidation: We had a discussion around how this strategy works, and why breaking down the number being subtracted into it’s expanded form is so effective (because the students could do the work in their head, because it is using friendly numbers, because it’s easier…).  The students named the strategy the FOOT LONG SUB – TRACTION strategy because you are breaking one number into it’s expanded form (which is quite long) and so the subtraction becomes three steps instead of one (also long).

Homework: Do the following questions using the Foot Long Sub-Traction strategy (only 5’s do the ones with stars beside them).

Today’s problem (Nov 7):

The students pulled out the important information:

Some students used the Foot Long Sub strategy:

Some students used the traditional strategy:

Consolidation:  We focused our conversation around a question they did to activate their brains before the problem.  They were asked how they solved 23-11 in their heads.  Some students said they changed the 11 to a 10 and then took one more away from the answer(23-10=13-1=12).  Other students thought 11+?=23, and they know that 11+11 was 22, so the answer must be 12 (11+12=23).  Others broke down 11 to 10 and 1 (23-10-1=22).  They were then asked to apply these ideas to today’s problem.

The word we focused on today is that subtraction = the DISTANCE between numbers.  You can change the numbers around to make them more friendly, as long as you keep the distance between the numbers the same.

23-11= The distance between 11 and 23

             11                                                         23 
               l________________________l
 If you move the 11 to a 10, in order to keep the distance between the numbers the same, you have to move the 23 to 22.

In other words, the distance between 11 and 23 is the same as the distance between 10 and 22, but 22-10 is much easier to do in your head!

23-11=22-10=12

Applied to todays question the student pointed out that:
951-305 is the same as 946-300 because the distance between the numbers is the same (but one is much easier to do in your head).

Fun with numbers 🙂

Today’s problem (Nov 8):

We activated our brains by asking the question, what subtraction question is being asked here:

Here was today’s problem:

At first the students thought it would be very difficult because of all the numbers, so we pulled out the information we need to know:

Some students were not paying attention 🙂
They realized their mistake (aha) after a short discussion…

There were two approaches used to solve the problem.  Either groups used only subtraction (all the students – jr. choir – pr. choir = audience):

Or the students added the two choirs together and then subtracted that from the total number of students:

Consolidation: We focused our discussion on comparing the two approaches.  We also reviewed the idea that subtraction is the DISTANCE between two numbers.

Today’s problem (Nov 9):

To get their brains active, they were asked to solve this problem in two different ways (not traditional):

465 – 128 =

This is what they did:

Today’s problem:

(numbers in black for grade 5’s, numbers in red for grade 4’s)

Some students solved this very complex problem in a number of different ways:

Consolidation: We had a discussion about the different approaches that could be taken to solve this problem (adding all the balls, taking away the damaged ones, then subtracting this number from the maximum number; working on each group of balls separately; etc…).  It was a lot of fun listening to the students explain how they went about solving this complicated problem.

Today’s problem (Nov 14):
(and the important information pulled out as a group)
(prices in red are for the grade 4’s, in black for the grade 5’s) 

Some students solved the problem by first adding all the bill together to get the total amount of money, and then subtracting the items bought one at a time:

Other groups added all the bills to get the total amount of money, then added all the items bought to figure out the total cost, then subtracted the cost from the money:

Consolidation:  We had a discussion around the importance of really understanding the question before attempting to solve the problem.  We focused on strategies the students could use on tests (and such) to make sure they pulled out all the important information before solving a problem (underlining, highlighting, etc…)

 

 

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