Addition Algorithm Rote or Understanding
Lesson 9 of 12
Objective: SWBAT relate the addition algorithm to rounded estimates and understand that they are adding tens and ones, which are different units.
Today I begin with a review of yesterday's lesson. The process of adding vertically (where we added the ones and then the tens) and relating 2-digit numbers to the closest number ending in zero (the smiley face number) was introduced in the previous lesson. I want to reinforce the process that students worked with so I begin writing the following problems on the board vertically:
42 + 34 = and 40 + 30 =
I ask students to solve the problems in their small math journal books. Next I ask for volunteers to come up and show us how they solved the problem. If the children did not use the columns, I may ask for additional volunteers to come up and show us their method. I will reinforce the adding of tens and ones.
Now I ask if students notice anything about the 2 problems? One is the smiley face equation for the other. If students do not notice, I may point out the 42 and 40 and ask if they notice anything. I will repeat with the 34 and 30, and with the answers.
I tell students that today we will begin by working with number equations for adding tens and ones, and equations with their smiley face friends to see if we can match the two up.
Playing A New Game
I have created a concentration game. I want students to attend to the structure of a 2 digit number and the related smiley face number that ends in zero (MP7). The problems can be mounted on card stock to make the game more durable. I create enough game sets so that there are no more than 4 students in each group. I wrote numbers between 10 and 99, making 16 cards randomly with no numbers ending in zero for the blue index cards. I now make 16 yellow index cards that are the smiley face pair for each blue number. When I wrote a 22 on a blue card, I wrote 20 on a yellow card. When I wrote 89 on a blue card, I wrote 90 on a yellow. I was careful to make sure that the blue numbers would not be friends with the same yellow (i.e. I did not write 39 and 41 on blue cards because they would both match a yellow card of 40).
I gather the students on the rug around me and I share the new game. I show the students the math problem cards and the smiley face cards. I tell them that they will try to match the two, and that they must try to remember where things are. I place the blue equation cards on the floor in a grid pattern. I place the yellow smiley face cards in a second grid pattern. I turn over 1 card in each grid. I see if the smiley face numbers match the equation card. If they do I get to keep them, if not I must return them face down from where I found them. I ask a student to be my partner and do the same thing. We each take 1 more turn as the others watch and ask questions.
I divide the students into heterogeneous groups of 4. I give each group a set of blue and a set of yellow cards to lay out on the floor. Students play the game for about 10 minutes while I circulate around watching the game. If I feel that students are not clear on how to match the cards, I may stop the groups and try to reexplain what they are trying to do.
I have the students return to their desks. I ask them if they think they can add larger numbers vertically independently. I tell them that it is ok if they are not quite ready to do this alone but I just want to get a feel for how comfortable people are at this point. I ask for a thumbs up if they feel comfortable, a thumbs half way if they feel that they can probably do it, but might need some help, and a thumbs down if they feel that they are not yet comfortable with adding vertically. This allows students to think about their own learning and it is a quick check for me about how students are feeling.
I tell students that they will work on a practice page. tens and ones practice.docxThe page has regular 2 digit number addition problems and next to them are smiley face number problems. The smiley face problems are the friends of the first problem. I did not fill in the smiley face friends for the last couple of problems but I hope that students can do it themselves.
I invite anyone who would like to work with me on the paper to bring a clipboard and a pencil and come to work with me on the rug. I tell the other students that I will hand them a page and they can work independently to complete the work.
At the board we do each problem together. I ask for volunteers to come up and write the numbers in as I write the problems on the board. I help students who need support in adding or deciding on the smiley face numbers. We add the ones and then the tens for each number. Students are looking for the regularity of the pattern of how adding with tens and ones works (MP8).
After both the independent group, and those who have worked with me have finished their work, I invite students to turn their attention to the white board.
I put the 2 problems where the smiley face numbers were not already filled in on the board. I ask students if they can solve the problems. Volunteers come up and fill in the problems. Together we check that the smiley face numbers and the original equations are close. If they are not, we try to figure out where we might have made a mistake.Reviewing Our Work