Soaring Skyscrapers: a Division Lesson

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Objective

SWBAT use a model to determine the height of a given number of floors in a skyscraper of a particular height.

Big Idea

Repeated addition can be used to solve a division problem.

Opener

6 minutes

To get students engaged in thinking about the height of buildings, I ask them to estimate the distance between the ceiling and floor in our classroom, and then estimate the height of our school. 

Then you might ask them about the height of a few well-known landmarks in your city and town. This could be known bridges, statues, trees, flag poles, etc. as well as any iconic buildings. Correct estimates are not necessary, but reasonable estimates should be strongly encouraged.  (No building is a million feet tall, and so on.)

The students fill out the Soaring Skyscrapers Entrance Ticket. You could do this, or have your students discuss the questions.  This will help them to start thinking about the relative height of buildings, and it will also help them to think about larger numbers, especially if, as with my students, they don't live near any particularly tall buildings.

Direct Instruction

5 minutes

It is important to remind students that division equations are like all other operations - there is no one correct way to solve.  That was the old school way of teaching division!  Students were expected to use the standard algorithm, period.  

With the Common Core, students are encouraged to develop strategies that match their skill level in order to solve with understanding (MP1). Just as repeated subtraction can be used to solve division problems, so can repeated addition. 

Today, we work with friendly numbers (1, 2, 5, 10), multiplication, and repeated addition to solve division problems. I model this by going through a few examples using simple numbers. The point of modeling, step-by-step with metacognitive narration, is to develop student thinking, not confuse it. For example, in this first example, after presenting the problem I would muse as to how I could use friendly numbers (2, 5, 10) to decompose the number using expanded notation (MP7). So, when considering:

27 ÷ 3 = 
(5 + 5 + 5) + (2 + 2 + 2) + (2 + 2 + 2) =
15 + 6 + 6 = 27

54  ÷ 9 = 
(5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5) ) + (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = 
45 + 9 = 54

98  ÷ 7 =

(10 + 10 +10 +10 +10 +10 +10 ) + (2 +  2 +2 +2 +2 +2 +2) + ((2 +  2 +2 +2 +2 +2 +2) =

70 + 14 + 14 =

 

Guided Practice

25 minutes

Students work through the examples in Soaring Skyscrapers Guided Practice on scrap paper or their whiteboards. When decided which format to use, consider what you need from this practice. Do you need a written product which can be analyzed to inform instruction? Or do you need a quick check, to inform instruction in the moment?

As we go, we discuss our work as a whole group. Remember, if you wait until the end of this work to discuss, students with errors or misconceptions will be practicing the again, and again, and again before they (and you) learn there is a problem. So, although it may take a bit longer, the purpose of instruction isn't completion of a lot of problems, it is success in transfer of knowledge. Choosing to cover fewer problems, with greater depth, is my choice to ensure student success.

It is also important that I am open to exploring alternative strategies offered by students that are not in the brief presentation.

Independent Investigation

25 minutes

Some students may need more space than is provided on the Soaring Skyscrapers Independent Practice Page. I give them scrap paper, or let them work out the problems on their whiteboards. 

Part of the process is choosing and using inefficient/wrong numbers initially, and then having to evaluate whether or not they need to choose a larger or smaller number.  Students will choose incorrectly at the beginning, and this is okay because this is developing their number sense. 

With practice, they develop a much better intuitive sense of which numbers are reasonable partial quotients and which are not.

Wrap-up

5 minutes

Time permitting, ask students to create a simple problem that they could use to demonstrate this strategy to someone at home tonight. 

An alternative: ask students what works (what they liked) and/or what doesn't work (what they disliked) when using this strategy, and why!