Monday, 23 June 2014

Addition and Subtraction Real-World Links

Teaching the operations (+, -, x, / , =) is one of my favourite things to do - apart from mountain biking, watching baseball live and singing in the car of course, which I guess makes me a three quarters nerd instead of a 100% nerd. Geez, I just put a % sign in that first sentence, who am I kidding - I'm a 100% nerd.

There are just so many different activities and most are not only very enjoyable and engaging to teach and do, but almost all also incorporate elements of real life and motivate students to continue learning after the bell. The actual sequence of teaching the operations, I do not propose to tackle here in this post. Suffice to say, I always model to and require my students to:
- estimate their answers first using the largest place value and some rounding
- use bundling sticks and MAB (which I call 'place value blocks' in class), particularly when renaming is involved, to show what the algorithm actually means, even before introducing it
- explicitly link the use of the algorithm and equal sign to materials and the worded, real-life meaning of the operation.
However, the actual sequence for the teaching and learning has been covered in detail by much more reputable people than I (more info coming in the next post or two).

This post focuses on different, engaging ways to practice the operations after modelling and alongside those materials, in the context of a sequential unit based on students' abilities. Indeed, many times during this unit, students actually had to be forced to pack up because they wanted to keep doing the task, even with the bell about to sound or having already gone. "Get out of here, you do know it's home time? Yes, well then why won't you get out?"

Here's a list of some addition and subtraction tasks from the units our class has just completed, roughly in order:

Scroll addition

I started addition using the jump strategy, where students learn to break up numbers into tens and ones for improved mental addition and subtraction. As part of this, students created scrolls using long thin strips of paper, adding 10 at a time to a number, or more, depending on their skills based on the pre-test, e.g. struggling students used MAB and practiced bridging and place value as part of this task, higher students started by adding numbers like 75, or 150, or 2,025 to a thousands or ten thousands starting place and many highs used both the jump strategy mentally and algorithm on paper (as a double-checking device) for their answers. Here's a pic of some of the finished products:


Number plates in the school car park
                                              Just another day in the school car park!
This is a classic and by no means by own invention, I got the idea from a colleague at my last school but I believe many teachers use the wonderful resource that are number plates for math and an extra opportunity to learn outside. Pretty much, it's as simple as having students add the numbers on the plates together, or subtracting a smaller plate from a larger one.

Of course, the lesson doesn't run smoothly simply by stating that. Prior to going out, I remodelled the focus on renaming, whether it was addition or subtraction or a mixture of the two for an extra show of versatility and understanding of the different renaming processes involved. For extra challenge, the students in my higher group (ranked according to the pre-test at first and then others earn membership according to their performance during the unit) added decimal points into the numbers prior to solving the equations. All students were to estimate the answer first; a process I require throughout the operations. At first, I get students to round the numbers for estimating according to the highest place value and, as the fluency and understanding of each student develops, I have them simply make an estimate based on their developing understanding of front-end place value.

Below is a picture of what my modelling for addition typically looks like, as replicated by one of my students in their grid book. Of course, almost all students in my class - grade three - use MAB at first in combination with on-paper workings, until they beg to progress to just showing their working out on paper or they clearly are ready for that.


The beauty of this task it that you'll find that some students will come in the next day with workings out from their way home or drive to the shops, showing all the number plates they added or subtracted along the way.

Footy scores - how did ... win by? 

This is a total winner amongst most grade three boys in my grade and as simple as printing out or projecting a page of the scores from the weekend for the latest AFL rounds (easily available online at   Fox Footy in a very printable/print-screenable format). Also works with pretty much any sport, except boring old soccer (seriously, 3-1, that's not even worthy of second term preps). It also embeds the concept of subtraction as the method for calculating the 'difference between' or 'how much more'. This task also reinforces placing the larger number at the top of the algorithm.

While most of the class engaged in this task, I took this consolidation time to teach my higher students renaming over zeros and had them create fantasy match scores suitable to practice this skill.

Races to zero (or another set number)

Basically, choose a number for a pair of like-ability students to 'race to' either by pulling out numbers using cards (two digit or more depending on ability) or by rolling numbers using dice. For example, a pair both start at 1,600 and race each other to zero by pulling out two digits at a time, creating a number and subtracting it from 1,600 and then from their latest total. You can also switch it around, e.g. racing from 250 to 10,000 using four digit additions. It is very quick and easy to differentiate, basically choose the number and number of digits to subtract per turn based on the pre-test or skills thus far in the unit, have students start at different numbers and different amounts of digits to add and subtract and move through a list of escalating difficulty as they go. For clarity:

A. Start at 132, race to zero, two digit numbers at a time

B. Start at 510, race to zero, three digit numbers at a time

C. Start at 1,340, race to zero, three digit numbers at a time

D. Start at 10,780, race to zero, three digit numbers at a time

E. Start at 50,600, race to zero, four digit numbers at a time

E.g. Eric, you work with Derek, start at D. Bianca, work with Sandra, start at B. (Some students didn't even do this task, they'd mastered this by the time we'd got to it, so I started working on decimal place value using

To add to the fun effect of this one, I had each pair use cars and at times during the lesson, move the cars to show their place and progress towards zero relative to their partner's. Mostly though, the concept of a 'race' was enough to get a great amount of engagement and motivation, and with that many sums and great fluency during the session.

Shopping, real estate, golf par/score cards and perimeter

                                                         I'll have that one thanks!

"What is that crazy woman doing running away with all those real estate/shopping brochures/golf score cards?" Brochures are absolute gold for addition and subtraction.

What's the total of the page? Pick three items to purchase and tell me the change you receive from $20?

Buy yourself a home and a holiday house, what's the sum of your real estate holdings? (Kids absolutely love that one, particularly when you hand them their own real estate booklet, many decided to take theirs home and keep working on it for hours that night).

How many metres long is the first nine holes, assuming I walk straight from the tee to the hole? What about if, on each hole, I walk an extra 75m to chase around my lousy shots?

You don't even need to have the kids waste time cutting and pasting from the brochures - don't make it an art task, it's math - and many students actually asked, before I instructed it, if they could just write down the numbers rather than cutting and pasting the pictures into their books.

Linking the concept to perimeter and measuring objects around the room and school yard is yet another way to make it real, and link two math concepts.

Worded problems 

I use a bank of worded problems, some sourced from the net, others I've created because it was simply quicker than searching one up and it was easier to create for my kids' needs. There are thousands of worded problems available online and in textbooks, but be sure to choose challenging ones (containing multiple steps, irrelevant or overload of information and that don't make it clear which operation is at play without students having to apply a fair amount of understanding to ascertain that). Remember, one quality worded problem solved using in-depth strategies, beats 20 ordinary ones any day.

I also have students practice creating their own worded problems from sets of equations, whilst solving these to continue to practice the algorithm too, which is generally more fun if you emphasise that the problems can be as crazy and hilarious as their imaginations can allow for:

e.g. Homer recently ate 522 donuts and 677 hot dogs, however, he soon puked up 167 donuts and 252 hot dogs. How many were left in his stomach?
355 donuts were still in Homer's belly, what a pig!

                                                                I'd do it again.

Multiplication and division posts are on their way next term. How do you teach addition and subtraction in your classroom?
How What activities or tasks do you use during these units? 

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