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The students will be able to explain why addition and subtraction strategies work, using place value and the properties of operations.

Big Idea

Students will be able to explain using concrete objects, pictures and words (oral or written) why addition or subtraction strategies work.


20 minutes

In this lesson I want students to be able to explain why addition and subtraction strategies work, using place value and the properties of operation. 

Since my students have worked with these skills in isolation, I want them to be able to use them interchangeably to gain a deeper understanding of how they work together mathematically. I ask a couple of volunteers to illustrate and explain how the properties of addition work.

See: Properties of addition 

As they are up explaining and illustrating how the properties work, I encourage students to ask questions. Students seem to understand how this process works.

To test it a bit more I write a word problem on the board. I remind students to apply both strategies to see which one works best for them.

There are 26 birds in the park.  25 more birds arrive.  How many birds are there? 

I ask students to read it aloud with me. Then, I ask, what do we need to know, what information does the problem give us?  I give them about 3 minutes to turn and communicate with their neighbor strategies and ways to solve the problem. Some students explain why addition and subtraction strategies work by using manipulatives, drawings, and their own words.  I ask a couple of volunteers to write their interpretations on the board. We go over their suggestions, and I ask student volunteers to offer different ways to explain their findings mathematically (using math vocabulary). 

Some students do not know the names of the properties; however, they say regrouping addends, and regrouping. These are all terms that they know, but I want to gear them towards using the correct math vocabulary terms. 

Together, we came up with various solutions on how to solve this problem.

MP1- Making sense of problem in order to solve it.

I continue probing students and building their math vocabulary and communication skills.


20 minutes

Material: Student Task Sheet

In this portion of the lesson I want my students to practice communicating their reasoning to others. Also I want to incorporate appropriate vocabulary in order for them to effectively exchange different ways to solve problems.  MP6 - Attending to precision.

Materials needed: white board, overhead projector, or interactive white board for whole group instruction.  Student task sheets for small group or cooperative group learning.

Task Description

I give my students two story problems to solve and they will write and solve two similar story problems. (See the teacher model for more details.)  During this guided instruction I make sure to assess their understanding addition and subtraction strategies. 

Here is my story:

I had 8 dimes in my pocket. I spent 50 cents at a bubble gum machine. When I got home, I found a hole in my pocket and only one dime is left in my pocket. How much money fell through the hole in my pocket? How do you know?

I give students about 5 minutes to turn and discuss ways to solve the problem with their neighbor.  As students are working I walk around the room to observe what they are thinking. I make sure to make note of any misconceptions. When students are finished,  I encourage students to share and explain their strategies. They discuss what they needed to know, and point out how place value applied to this process (8 dimes means 80 cents). I make sure students discuss what they liked about the various strategies. (Most students point out that there are many different ways to solve problems, and they have a choice.)

I continue to support students in communicating using mathematical language.

See: Student Work Sample


15 minutes

Materials: Task rubric;  Students Task;  Instructional Task Directions 

In this portion of the lesson I ask students to return to their assigned seats to complete their exit task cards...  

Have you ever wondered about magic?  (Yes we have!) Well I am going to close my eyes and say the word Abracadabra five times really slow. When I open my eyes I want to see clean tables and neat floors. Can you all do that? (Yes!)  I begin to say Abracadabra…… I open my eyes and see a wonderful group of students sitting attentively on the carpet.  I give them big thumbs up!

To bring this lesson to a close, each student is given their own individual task sheet with an equation to solve.  They will be assessed using the following rubric to determine their individual level of mastery.   As students are working, I circle the room to check for understanding.  I want to see if they can correctly solve problems, use strategies such as place value, properties of operations with mathematical explanations.  I remind students to revisit their rubric to make sure all parts of the skills are being used. When students are finished, I ask them to pair up with their neighbor to share how they solve their problems. I notice some students use place value, and others used properties to help them solve. Students seem a little bit surprised that they can use different strategies, yet come up with the same answers. For other students just hearing students explain how they solve made them feel a bit more comfortable explaining their own ideas. 

Students worked on MP1 and MP6

Student work sample

Note: This task comes from a Wiki set up by the Public Schools of North Carolina.