Today I start by reviewing fact families with students. I present 2 equations from the same fact family. I write them on the board with ? for the missing numbers:
19 - ? = 11
11+ ? = 19.
I ask students to solve the two sentences in their math journals. I ask students if they notice anything about the 2 number sentences.
We discuss their observations. I am hoping that students will realize that the equations are from the same fact family and that solving one will give them the answer to the second. (This is a review of work earlier in the year, but now with larger numbers.)
I put up the following equations: ? + 35 = 60 and 60 - ? = 35. I ask students again to solve the problems and then we discuss what they have found.
I tell students that today we will work with fact families for larger numbers as we look for parts and totals in numbers.
I bring students to the rug to play a new game. I model the game first with one child as my partner. The other children sit on the edges of the rug to observe how the game is played.
I put out a board that has a square on it. The square is divided horizontally. The top half is labeled as the Total. The bottom half is further divided vertically into two smaller pieces which are each labeled as Parts. I ask students if they remember seeing the chart yesterday? Ok today we are going to play the game with these boards.
I will start, I draw 4 cards (cards from a regular card deck, using only the numbers 1 - 9). I use the cards to build 2 numbers. Then I roll a sign die (+ or - marked on all 6 sides). The roll tells me if I am going to add my two numbers, or subtract one from another. If I am going to add, I place the two numbers in my two Part boxes because students know that when they add they get a bigger number so the bigger space should be empty. If I am going to subtract I place the larger number in the Total box and the smaller number in one of the Part boxes because subtraction gives me an answer smaller than what I started with (unless the other number is zero) so I need to leave a smaller space empty. I write a number sentence for my numbers and sign on my white board. Now I use the calculator to find the answer. My partner must use another strategy from his/her suitcase to solve the problem. If my partner gets the correct answer, he/she gets one point. If he/she is incorrect no point is given and we switch roles. The game allows children to model with mathematics to help them understand the operation they need to perform and what they are aiming for (larger or smaller number) (MP4).
I have my partner walk through the steps this time.
I check for understanding from all the students. (Thumbs up if you could play the game, thumbs down if you are still not sure what is going on). When students are ready, I partner them up to play the game. I circulate around to check on how students are doing.
At this point all students have had a chance to play the game and to experiment with solving equations using the idea of Big, Small, Small parts. I now want them to explore using this strategy of their own.
Because there are diverse levels in the room, I have 2 different papers ready for students. One uses larger numbers than the other. These problems present 2 numbers and a sign. Students write the equations from the Big, Small, Small boxes and then record the strategy they are using to solve the problem. Children should be making use of the structure of the Big, Small, Small boxes to help them solve the equations. (MP7)
I circulate around the room to check in with individual students. If I see several students who are all still having trouble with moving the numbers to the graphic organizer and then into an equation, I will take them as a small group and work with them to be successful with the work.
Students respond to a sentence starter in their journals to help me assess their understanding of the reasons for using a variety of strategies to solve mathematical equations.
Sentence starter: When I choose a math strategy to solve a problem I think about ___________
or: I know how to pick a strategy to solve a math problem because ___________________