Addition

We started focusing on “addition” today.  We are hoping to develop a deeper understanding of what addition means, and how we can apply it to mental math strategies.

Today’s problem (Oct 19th):

Some of the students noticed that the word “about” was not included, and the students discussed what that meant.  The conclusion was…

Some students used drawings (base 10 blocks) to demonstrated how to add the numbers:

 

Some students connected our unit on rounding numbers, to the addition question.  They rounded (by adding 3 to 57 and adding 2 to 38 – and then took the 5 (3 and 2) away from the answer:

Some students used a number line:

Some students used the traditional strategy:

Some students made a connection between the traditional strategy and the work using pictures of base 10 blocks because the grouping of the ones (and changing them into a ten).

Consolidation:  We focused on one particular strategy.  In this strategy the numbers were broken into their expanded form (58=50+8 and 37=30+7).  The tens were added (50+30=80) and the ones were added (8+7=15).  Then the ones and the tens were added together (80+15=95).  The students named this strategy th BREAKDOWN strategy (because you break down the numbers into their place values):

For homework the students were given a few questions to do using the Breakdown strategy:

Today’s problem (Oct 20):

Then we talked about information do we need from the question, and the students came up with:

Some students solved the problem using pictures (base 10 blocks).  The students did a good job demonstrating how the grouping works when adding (10 ones make a ten, etc…):

Some students used the ‘Breakdown’ strategy:

Some students solved it using a traditional strategy:

Consolidation: We talked about some connections between strategies.  But a new strategy wasn’t used, so we looked at the following question together, and the students were asked to do the math mentally:

The students were asked, “What did you do in your head?”

Some students talked about breaking the number up into tens and ones:

Some students talked about how they would start at the biggest number and count up (by tens and then ones):

Some students talked about changing 13 to 15 because it was an easier number to work with, and then taking the difference away at the end:

The students were asked to keep these ideas in mind the next time they approach a problem.  It was a lot of fun!

The students were given a few more questions to practice the breakdown strategy.

Yesterday’s (oops) problem (Oct 24):

The students pulled out the essential information:

Some students used base 10 blocks to show the answer:

Some students used the breakdown strategy:

Some students used the traditional strategy:

Some groups used a new strategy:

note:  the 157 should be say 557 (oops)

Consolidation:  We looked at this strategy and the students noticed that one of the numbers was close to a friendly number (405 is very close to 400).  So the solution takes 5 away from 405 to make an easy number to work with (friendly 400), adds 152 (400+152) to get 552.  Then they put the 5 back (that they took away) to get 557.  The students named this strategy “Chunky Smoothy” because you begin with chunky (difficult) numbers, but then you change one to a smooth (friendly) number… chunky – smoothy

The homework questions were supposed to be done using the Chunky Smoothy strategy:

Today’s problem (Oct 25):

Hmmmm….

Some students used the breakdown strategy:

Some students used the Chunky Smoothy strategy:

Some students used a kind of chunky smoothy strategy, but they made BOTH numbers smooth:

Some students used the traditional strategy:

Some students had such a strong grasp of the meaning of addition that they showed all the strategies:

Consolidation:  We spoke about what happens in Mr. Wendler’s brain today.  I explained that in my head I only break one of the numbers down into it’s expanded form, and then I add it to the other number (one piece at a time).  The students were able to connect this strategy to all the other strategies.  They decided since only one number is being broken down, we would call this strategy “Breakdown Junior”.

Here is what it looks like:

Or it can look like this:

For homework the students were asked to do yesterdays problems again, but using the Breakdown Jr. strategy.

Today’s problem (Oct 27):

Today the question was meant to focus on adding more than two numbers together.  The question was:

Some students were clever and realized the question was not asking for the minimum number of trips 🙂

Some students put boxes on the forklift, and then opened the boxes up to remove the excess weight.  It opened up a discussion as to whether this is allowed 🙂

Some students simply carried two boxes at a time:

Some students started from the least amount of weight to see how many boxes the forklift could carry, and moved to the heaviest boxes:

Some students added up the hundreds column to get to 700 and then calculated the exact amount to make sure it was not over 800 kg:

Some students added the heaviest boxes first, and moved to the lightest:

Consolidation: We had an interesting discussion about the different approaches to the problem, and if one seemed more efficient or effective than another.

For homework the students were asked to answer:

Today’s problem (Oct 28):

Our questions are getting a little more involved.  This one also includes thinking about differences as well as sums.

The students pulled out the important information:

Some students solved the addition section by adding the dollars and cents separately:

Some students tried to find the difference between the total money raised (369.75) and the desired total (500.00) by using an addition question.  They tried to think about what digit they could use to bring each place value column to 10, leaving a 0 in the answer (except for the hundreds column where they needed a 5):

Some students started at 369.75 and slowly worked their way up to 500 by adding chunks of friendly numbers (100, then 20, then 10, then .25)

Some students used subtraction to find the difference (500.00 – 369.75)

Consolidation:  We had a discussion connecting the various strategies.

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One Response to Addition

  1. michael kelly says:

    cool
    me like break down m k

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