Problem set #10.
1) Sunny has 8 rolls of candy. Each package has 10 candies in it. She also has 12 extra candies. How many candies does she have in all?
2) Jack has 30 pencils. Emilio gives him 29 more pencils. How many pencils does Jack have now? (Is it enough for everyone in second grade to have 1 pencil?)
3) Danielle has 45 beads. She wants to make necklaces and put 10 beads on each necklace. How many necklaces can she make?
4) Use two strategies to solve:
30 + 40 = ______
25 + 20 = ______
60 – 20 = ______
20 + _____ = 31
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Problem set #9.
I decided to carry on with true/false number sentences, to help the children begin to use mental strategies involving tens, and to help them become comfortable working with symbols.
True or False?
10 + 10 = 5
5 + 5 = 10 + 10
10 + 10 + 10 + 3 = 33
33 = 10 + 3
10 + 10 + 10 + 10 + 10 = 100
22 + 10 = 32
12 + 10 = 10 + 12
10 + 2 = 5 + 5 + 2
2 dimes = 4 nickels
4 dimes = 10 pennies
As Megan Franke has described doing in her own work with elementary students, I wrote these number sentences on index cards so that I could easily shuffle through them as I was working with the children.
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Problem set #8.
We worked with the Candy Factory again and using number sentences to represent the situation.
1) a. Dr. E. has 4 rolls of candy and 11 loose candies. How many candies does she have altogether?
b. Dr. E wants Sunny, Daniella, Jack, and Emilio to share her candies equally. How many candies can each child have?
2)True or False?
10 + 10 is the same as 5
5 + 5 is the same as 10 + 10
10 + 10 + 10 + 3 is the same as 33
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Problem set #7
Candy Factory
At the Candy Factory, the candy packing machine puts 10 candies in each roll and 10 rolls in each carton.
Then, we solved some problems:
1) Mr. Diaz has 6 rolls of candy and 10 loose candies. How many candies does he have?
2) Ms. Principal has 110 candies. How many rolls of candy can she make?
3) Ms. Teacher1 and Ms. Teacher2 are buying candy for their classes. They want each child to have only 1 candy each. How many rolls of candy should they buy altogether?
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Problem set #6.
1) Daniella has 42 beads. She wants to make necklaces with 10 beads on each necklace. How many necklaces can she make?
2) Jack has 30 cents. Emilio gives him 52 cents. How much money does Jack have now? What could he buy with this much money?
3) Sunny has 11 packages of cookies. Each package has 10 cookies in it. She also has 5 extra cookies. How many cookies does she have in all?
I’m still using multiples of tens in the problems. (And no one yet as asked me why we work with multiples of 10 every week; a sure sign that we need to keep working with multiplies of 10 because the children don’t differentiate them, as a class of numbers, from other numbers.) I put bigger numbers here hoping that using individual tallies for all the objects would get tedious. And it did, for some.
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Problem set #5.
First we read a book called Only One, which emphasizes the mathematical big idea of thinking of several things as one thing (examples: 1 dozen is 12 eggs; 1 dime is 10 cents). I asked the children to fill in the blanks:
1 egg carton = ____ eggs
1 dime = ____ cents
1 ____ = ?
1 ____ = ?
Then we solved problems:
1) Emilio had 5 dimes to spend. He bought a _____ that cost 20 cents. How much money did he have left?
2) Sunny had 2 dimes. She wants to buy a ____ that costs 40 cents. How much more money does she need?
3) Dr. E has 70 cents. She spent 52 cents on a chocolate bar. How much money does she have left?
I chose these problems to continue to work on helping the children develop ten as a unit. As you will see, the money context posed some special problems of its own.
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Quick problems to begin session #4.
I began by holding up 3 sticks of 10 unifix cubes, and asking the children how many I had.
All but Emilio said 30. (Emilio was sharpening his pencil.) Then I held up 52, in 5 tens and 2 ones. That was a little harder for them to see, but basically they understood the tens and ones combination. (Sunny saw 42, Daniella saw 51, and Jack saw 52. Emilio was still sharpening his pencil!) Yet their understanding of the base-ten structure of double-digit numbers seems fragile, because they used very little of that understanding to solve these multidigit problems.
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Problem set #4.
Solve in at least two ways.
30 – 12 = ___
20 + ___ = 45
40 + 21 = ___
I wrote these problems without a story context to find out if children could connect numbers and context. It seemed from previous sessions with the children that they understood operations. Because they have been using a lot of strategies based on ones but not tens (for example, using tally marks), I used multiples of ten in these problems. Before the children started working on these problems, I made sure each child had 70 unifix cubes in groups of ten in front of him or her (we’ve been working on keeping them in tens).
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Problem set #3.
I wrote these problems as a follow up to assessing and developing base-10 concepts. Again I included the children’s names for interest. In hindsight, some of the problems were TOO DIFFICULT and I already have some ideas about how I will change them for our next session.
1) Daniella has 40 chocolate chips. She ate 15 of them. How many chocolate chips does Dominuqe have left? (Separate Result Unknown)
2) Sunny has 22 pennies. How many more pennies does she need to have 50 pennies to buy a book? (Join Change Unknown)
3) Jack has 60 cards in his collection. He gave away 26 cards. How many cards does he have left? (Separate Result Unknown)
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Problem set #2.
I wrote these problems to find out more about the children’s understanding of base-10 concepts.
1) For Valentine’s Day, Emilio got 4 rolls of candy. Each roll had 10 candies in it. How many candies did Emilio get altogether?
2) Sunny has 16 pieces of chocolate. Just to be nice, her friend gives her 20 more pieces of chocolate. How many pieces of candy does Sunny have now?
3) Jack has 30 dollars. How many more dollars does he need to have 45 dollars to buy a new bike?
4) Daniella has 55 tropical fish. She wants to put 10 fish in each bowl. How many bowls does she need for all of the fish?
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Problem set #1.
These addition and subtraction problems represent four different problem structures. These structures are based on CGI probem types. (For more information about CGI, see this book.)
1. Maya has 13 jellybeans. Her brother gives her 8 more jellybeans. How many jellybeans does Maya have now? Join Result Unknown
2. Jason has 28 pennies. He loses 13 of them. How many pennies does Jason have now? Separate Result Unknown
3. Eric is putting candles on a birthday cake for his brother. There are 4 candles on the cake so far. How many more candles does Eric need to put on the cake so that there are 7 candles altogether? Join Change Unknown [not given]
4. Sarita has 9 toy rockets. Her brother George has 6 toy rockets. How many more toy rockets does Sarita have than George? Compare Difference Unknown [not given]
Created during instruction: You’ve got 3 big bags of soccer balls. Each bag has 10 balls in it. You’ve also got 2 loose balls. How many balls do you have?
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