Lesson 5

Algorithms for Adding Integers

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Objective

SWBAT evaluate integer sums using an algorithm

Big Idea

We've used number lines and counters to model sums. Now it's time to use the most efficient method for integer sums - the algorithm.

Introduction/Reflections

15 minutes

This narrative goes with page 1 of the resource:   AlgorithmsForAddingIntegers_Module.docx

 

Before presenting students with an algorithm or procedure for adding integers, I want them to reflect on the work we have done over the previous 2 days.  The reflection serves as a review and a way to get students to use MP8 to transfer what they know about integer sums into an efficient algorithm.

 

Each question will be presented one at a time using a think-pair-share strategy followed by independent writing.  Using question 1 for an example we will: 1) Pose the question; 2) Discuss the question with partners; 3) Groups will share their thoughts; 4) Students will independently write.  I know there are some arguments for giving students a chance to think and write BEFORE having a discussion, but I think it is often helpful to reverse that format.

 

The discussion aspects of this reflection activity engage students in MP3.  During the "pair" I will pick a couple of groups to listen in on a conversation to bring up possible misconceptions and/or insights to present to the class as a whole during the "share".  During the "share" students will be sharing their response with the class or listening and evaluating the responses of others.  Students will be encouraged to snap in agreement or be prepared to improve on a response.  

Problem Solving

5 minutes

This narrative goes with page 2 of the resource:   AlgorithmsForAddingIntegers_Module.docx

 

The problem solving section gives students a chance to "figure out" the adding procedure by using a word bank to fill in the blanks.  I could just given the rule here, but I hope for kids to transfer some of their knowledge from the introduction to making sense out of the algorithm.  This section should go fairly quickly (hopefully).  But then, I would like to have some brief discussion where we connect some of the ideas from the reflection to the algorithm.  

So we will quickly find which problems from A-F support our answers to questions 1-6 on the introduction/reflection section.

Independent Practice & Extension

20 minutes

This narrative goes with pages 3-4 of the resource:   AlgorithmsForAddingIntegers_Module.docx

 

The independent practice consists of 8 problems which are intended to help students practice their fluency with the algorithm.  I tried to make the values large enough so that a model would become impractical.  If students insist on some form of modeling, I will encourage them to use the model as a way of seeing if their answer makes sense (MP4).

 

Some students may have a difficult time when they see 3 addends like in problems 7-8.  I would ask them to think of an easier addition problem of addends (like:  1 + 2 + 3) and then ask how they would evaluate that.  When we go over the answers, I will be especially interested in hearing how students solved 7 & 8; which students use the commutative property to first add numbers of the same sign or some other combination.  For example, on number 8, you may see the sum -19 + 26 + 14 as -19 + 40   or  7 + 14   or -5 + 26.   This would be an example of MP7.

 

Every student should easily make it to the extension.  Problem 9 is not particularly difficult but some of my students will likely complain that there is "too much to read".   This will be an opportunity for students to persevere in problem solving (MP1).  Sometimes a lot of reading is required to understand and solve a problem, I will say to encourage them.  I have placed the dollar amounts in bold just to make it a bit more manageable for some.

 

For problems, 10-13 students are asked to make fact families using addition or subtraction.  I want to give students a sneak peak at integer differences and remind them of the relationship between addition and subtraction.  

 

The extension ends with some simple equations that can be solved using mental math or fact families.  My guess is that most students will need to apply fact families.  If a students can solve the equation in any valid way, that is fine too, as long as they can explain their method.

Exit Ticket

5 minutes

The first two exit ticket questions assess whether students understand how to make sums using different signs.  The third exit ticket is to see if students can see that the variable C must be a negative number because the sum is negative and the known addend is also negative.  Of course, 1 & 2 have an infinite number of possible answers while 3 only has 1 unique answer.