SeptemberWeekOne

Day 1: Do a story problem based on a story told by achild. (A goodpractice to follow allyear). For example, Kyana told a storyaboutwinning a fish at a wedding. Iasked, “Who has fish at home?” I chose3children whose total fish added up to 10. I drew fish tanks for each child’s house and put inside ithow many fishthey said they had. Then Iasked, “How many fish do Kyana and Charlieand Ramon have altogether?” Children showed their answer on theirfingers(I didn’t call on individual children until I saw everyone’sanswer on theirfingers -- remind them not to look at each other’sfingers.) Then ask, “How many //groups//offish are there?” Many children willstill answer 10. Re-state thequestion:“How many tanks with fish in them are there?” Keep using thelanguage of //groups//interspersed with the language of tanks. Repeat the questions, alternating between asking how many //fish// there are and how many //groups//of fish there are. Call on individual children at thispoint. They cancome up and count on theboard if they need help to answer the questions.

Day 2: Bring 8 glue sticks and 2 baskets to the rug. “One of the jobs teacher have at the beginning of the year,when theyget ready for school to start, is to organize the supplies, thingslikepencils, glue sticks, scissors, etc. Here are some glue sticks toorganize. How many glue sticks are there? Show me on your fingers andtry not to look at each other’s fingers.” Put 4 glue sticks in each basket, lined up so the kids canstill see each individual glue-stick (not in a clump). “How many //groups//ofglue sticks are there? How manybaskets with glue sticks in them?”Repeat the questions like the day before, alternating between howmanyglue sticks there are and how many groups of glue sticks. Other things may come up, such as 4 + 4 = 8, in which case Imentioned that yes, that is a //double//,anddoubles are very important. I alsomodeled writing a few equations onthe board, which some children will followand others won’t, and I wroteboth addition and subtraction equations on theboard because so oftensubtraction is overlooked. Then bring out 13 pencils and 2 cups. Lie the pencils down in a big pile on the rug(so they can’t be counted). “Let’s organize the pencils now. Who can make an //estimate//of how many pencils there are? Who can make a good guess of how manypencilsthere are?” I write the estimates on theboard with the child’sname next to the them. “Let’s put the pencils in groups. Who can come put 5 pencils in onecup? Now who can come put 5 pencils in the othercup?” I also draw thecups with 5pencils in each one on the board, and 3 extras outside thecups. “Can we make another group of pencils? Do we have enough pencilsto fill another cupif each cup has 5 pencils in it?” Children answer no. “How many pencils are there?” Discuss different ways to count: by ones,byfives to ten and then by ones, or some children just know that 5 +5 =10 andthen they count on 3 more. Count all theways and make sure youalways get the same answer. Look back at the estimates to see whowasclose. “How many groups of pencils are there? Remember these ones on the floorare not in agroup, they are extras. How many groupsof 5 pencils arethere? How many cupswith pencils in them are there?” “Now, how many //extras//are there? How many pencils are therethat don’t fit in a group?” Again, repeat the questions, alternating between how manypencils, how many groups, and how many extras. It might be a good idea to begin a chart that has heading ofTotal,Groups, Extras that you can fill in as you continue to do problemslikethese. Teach the games Staircases and Double Compare. Children with lessexperience comparingnumbers should do Staircases; those who have asolid understanding of numberunder 12 don’t need to do it and canpractice Double Compare. When you demonstrate Double Compare, counton,and see if they try it out when they play, instead of counting all.

Day 3: “Today we are going to think about things that come ingroups: a groupof things that are all the same. On one hand, how many fingers dowehave? Show me with your fingers.” Some may answer 10, so repeatthequestion. “So that’s //one group// of //5 fingers//.” Show a picture of a bicycle, or draw one on the board. “Here is 1bicycle. How many wheels does it have? Show me on your fingers. Right,so this bicycle has //one group// of //2 wheels//.” Repeat with atricycle. “Who can think of other things that come in groups?” My kids only thought of body parts, which mostly come in2s. I wantedsomething that came inlarger groups also, so my assistant teacher askedthem to think about pets theyhad at their houses and their body parts.We talked about cats, who have 4 legs. Draw two cats on the board (or whatever else they come upwith that hasabout 4 in its group. It’simportant to go with their own stories orideas). “Imagine we are taking Diana's 2 cats to the vet to get theirclaws cut (their fingernails cut). Oooh,they do //not// like to get their nailscut! Who wants to be the vet?” One child comes up to the board to be thevet. “Alright, Ti is going to be the vet and cut the cats’nails. Go ahead,Ti. When you cut one, circle it on theboard.” After he circles 3,stophim. “Ok, so how many feet did Ticut? How many more does he stillneed tocut?” After that, repeat those questionsafter each additionalfoot, so you go through the list of how many he did andhow many more heneeds to do. This istheir introduction to decomposing numbers. Then, children go off to do Staircases, as described in //Investigations//, or Double Compare. Some children may need to play single Compareas well.

Ideas for practice for decomposing numbers: Usingfingers, show different ways to make smaller numbers (under 5) How Many ofEach? problems Snap It! Paper ClipCombinations (do all the ways to make one number one day, etc.) Build it in2 Parts (see above) Tens GoFish (or similar games) NumberSandwiches (53) I Wish IHad (51) Counters ina Cup MissingPart Cards Day 4: Introduce decomposing numbers and kids go off to do itthemselves. “Let’s pretend you work at an apple orchard with lots ofapples growing.Your job is to pick 7apples and put them in two baskets so you can sellthem at the orchardstore. Let’s draw the 7 apples. (Draw them on theboard.) Hmm, now is this math class or artclass? Right, so right now Iam tryingto get better at math work, not at drawing. So instead ofworking hard to draw perfect apples, I’m just going todraw circles.”Give this message earlyon and keep reiterating it throughout the year.“If I spent a lot of time drawing really nice apples, I wouldbepracticing my drawing, but not my math learning. And mathematiciansalways try to do thingsefficiently, which means they try to find thequickest way they can to do agood job.” “Now who could come up and put some apples in one basket andsome applesin another basket? Why don’tyou draw circles around the apples that gotogether in one basket and theapples that go in another basket?” “So, you put 3 apples in one basket and 4 apples inanother basket. 3and 4 go together tomake 7 – it’s like inside 7, 3 and 4 are hiding!Let’s see if we can find any other numbershiding inside 7. Who can findadifferent way to put the apples in the baskets?” Alternatively, have real apples and baskets and have thekids move themaround and find a few different combinations of 7. Record on the boardwhat they are doing,using circles for apples and circling them forbaskets. (Maybe do this twice or 3 times). Send kids off to work onfinding more ways toorganize their apples on their own. END OF CLASS: Share ways to organize apples, making a list on the board of combinations they came up with.

Day 5: Choices: Compare / Staircases for some Snap It! /Double Compare for others END OF CLASS: "I went outside and saw 3 tables. Each table had 2 apples onit. How many apples were therealtogether?" Talk about different ways to count: by ones, by twos, 3 + 3, 4 + 2, etc. "How many groups of apples are there? How many tables with apples onthem? How many apples?" Repeat questions to different students.