Houghton Mifflin Math Problem Solving. (2007). Retrieved September 15, 2012, from

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1 Topic: Subtraction (Lesson 1.9 on website) Draw a picture Grade range: 1-2 Jenny has 12 balls and 8 of the balls are blue. The rest of the balls are red. How many red balls does Jenny have? Jenny has 4 red balls. A possible method to solving this problem for students would be to draw out the problem. First the students could draw 12 balls. Then the students could count out 8 of the balls and color them blue, and then color the left over balls red. The students could then count the red balls. This problem helps students practice the strategy of drawing a picture to figure out a problem. Although, this problem may seem simple to most to a 1 st grader or 2 nd grader it could be difficult. Thus, drawing a picture would help them figure out the subtraction problem. This problem is also framed to encourage students to think-addition which means instead of the student asking what is 12 8 the student would ask what goes with 8 to equal 12. Houghton Mifflin Math. (2007). Retrieved September 15, 2012, from

2 Topic: Subtraction (Lesson 3.8 on website) Act it out Use manipulatives Grade range: 1 There are 8 birds sitting in a tree. Then 3 more birds came and sat in the tree. How many birds are now sitting in the tree? There are 11 birds sitting on the tree. A possible method to solving this problem for students would be to act it out with classmates. For example there could be 8 students acting as the birds sitting on the carpet. Then one student would direct 3 other students to come sit on the carpet (fall off the tree). Then the student counts how many people are now sitting on the carpet. Another possible method to solving this problem would be to use manipulatives. A student could have a picture of a tree and place manipulatives (blocks, bears, dots, or buttons etc.) as representatives of the birds. The student could place 8 manipualtives in the tree and then put down 3 more. They could then count the total to get 11. This problem helps students practice the strategy of acting out a problem or using hands on manipulatives. Although, this problem may seem simple to most to a 1 st grader it could be difficult and confusing. Thus, it is helpful for the students to act out the problem or use manipulative to actually see the problem take place in front of them. Houghton Mifflin Math. (2007). Retrieved September 20, 2012, from

3 Topic: Probability (Lesson 9.6 on website) Use a picture Make an organized list Grade range: 1-2 Paul has this bag of marbles. Which kind of marble is Paul most likely to pick from the bag without looking? Paul is most likely to pick the striped marble. A possible method to solving this problem is for the students to count each type of marble in the bag and make an organized list. This maybe challenging for some students to distinguish and categorize each marble and count correctly. The picture would have to be much bigger. Some students may even use manipulatives to represent each type of marble and recreate the picture. This problem helps students practice the strategy of using diagrams or pictures to help them answer a problem. This problem is also helping students to begin to think in probability terms. This could be a way to introduce students to the idea of probability. Houghton Mifflin Math. (2007). Retrieved September 15, 2012, from

4 Topic: : Number Sense/ Hundreds chart patterns Find a pattern Grade range: 1 Missing numbers: Provide students with a hundreds chat on which some of the number cards have been removed. The students task is to figure the missing number or ell what they are. Have all the columns of even numbers missing st column: 2, 12, 22, 32, 42, 52, 62, 72, 82, 92 2 nd column: 4, 14, 24, 34, 44, 54, 64, 74, 84, 94 3 rd column: 6, 16, 26, 36, 46, 56, 66, 76, 86, 96 4 th column: 8, 18, 28, 38, 48, 58, 68, 78, 88, 98 5 th column: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 A possible method to solving this problem for students would be to find a pattern within the missing numbers. Some students might go through each row and fill in the missing numbers that way by counting by ones. Some students my start that way and figure out there is a pattern within the columns. Some students may realize that the missing numbers are all even numbers This problem allows students to see the patterns within the hundreds chart that are not obvious to them yet. This problem can be done various ways with many different

5 Alison Wheeler patterns. This problem will help students to recognize patterns within numbers and develop place-value concepts, odd and even concepts, and number concepts. When students are describing their solution the teacher should encourage students to thinkaloud to describe how they made their decisions and what key features of the numbers they think about as they place the number properly on the chart. Van De Walle, J., Karp, K., & Bay-Williams, J. (2013).Elementary and middle school mathematics: Teaching developmentally. (8 ed., p. 205). Boston: Allyn & Bacon.

6 Topic: Subtraction (Lesson 4.6 on website) Use a graph Use manipulatives Grade range: 1 Blue How many people like blue and purple in all? Which color has more votes blue or yellow? How many more? How many more votes would the last place color need to become the first place color? Favorite Color Purple Yellow 5 people like blue and purple in all Yellow has more votes than blue by three votes Purple would need 4 more to tie yellow and 5 more to take first place A possible method to solving this problem for students would be to use the graph. Students could use the graph and count the squares to determine the answers to the problem. To solve this problem students could also use manipulatives to represent a physical graph in which they could touch, manipulate, and move around. This problem helps students practice the strategy of reading and understanding the information presented in a graph can be analyzed and understood. This problem could be a challenge for some students when it comes to determining how many more or what is needed for last place to become first place. Houghton Mifflin Math. (2007). Retrieved October 11, 2012, from

7 Topic: Making a table (Lesson 4.6 on website) Make a table Use manipulatives Grade range: End of 1 st / Beginning of 2nd Noah saves two dimes each week. On the 3 rd week Noah was given an extra nickel for mowing the lawn. How much money will he have saved at the end of 3 weeks? Week Money Saved 1 20 Cents 2 20 Cents 3 25 Cents Total 65 Cents A possible method to solving this problem for students would be to make a table. Students can look at the problem and determine how much money for each week. Manipulatives could be provided for students to use to visualize how much money Noah would be saving within each week. The problem is more difficult because Noah does not just receive two dimes each week the pattern changes in the 3 rd week with an extra nickel. This problem helps students practice the strategy of recording and placing data in a table. The table helps students organize the data and determine which operation to carry out. This problem would be more towards the end of first grade going into second grade. Houghton Mifflin Math. (2007). Retrieved October 27, 2012, from

8 Topic: Using a Number Sentence/ Making a Table (Lesson 5.5 on website) Write a number sentence Make a table Use manipulatives Grade range: End of 1 st / Beginning of 2nd Trevor feeds 3 cats on Monday. Then he feeds 10 more cats on Tuesday. How many cats does Trevor feed in all? Trevor feeds 13 cats in all. A possible method to solving this problem for students would be to create a number sentence. The student would have to choose either addition or subtract and write it in a number sentence to be able to solve it. The student would find the two parts in the problem to create a whole. o = 13 Another possible method to solving this problem is for students to create a table. Students can look at the problem and determine how many cats Trevor feeds on Monday and then how many he feeds on Tuesday. Then they could organize the data and see how the parts become a whole through addition. Trevor s cats Monday 3 Tuesday 10 Total 13 o Manipulatives could be provided for students to use to visualize how many cats Trevor would be finding on Monday and Tuesday. A beaded number line would be a good manipulative for students to use for this problem since it deals with addition and place value. This problem helps students practice the strategy of writing a number sentence, recording and placing data in a table, and using manipulatives to help them solve a problem. It is important for students to know how to choose what operation to solve the problem and

9 Alison Wheeler how to write it in a number sentence. The table helps students organize the data and determine which operation to carry out. Houghton Mifflin Math. (2007). Retrieved November 4, 2012, from

10 Topic: Stoplight Problem Use a picture Make and organized list Find a pattern Use manipulatives Grade range: 1-2 (May be more appropriate for 2 nd and challenge some 1 st grade students) How many different stoplights can you make? Each stoplight must have a red, yellow, and green light in it. 6 different combinations can be made using red, yellow, and green R R G G Y Y Y G Y R R G G Y R Y G R A possible method to solving this problem for students would be to create a picture of all the possible combinations. Students could draw stoplights and use crayons as the light colors. This would allow students to work through the problem and visually see the combinations happening. Another possible method to solving this problem is for students to create an organized list. If students do not need the visual but would rather write it out then they can create and organized list like the one below. o 1: R, Y, G o 2: R, G, Y o 3: G, Y, R o 4:G, R, Y o 5: Y, R, G o 6: Y, G, R Creating a picture or an organized list would also lead some students to discover a pattern. Some students may discover if you put each color on top of the stop light twice and switch the other two colors you will get each combination.

11 Manipulatives could be provided for students to use to visualize how many combinations a stop light can make. Using blocks such as the unfix cubes would allow students to physically manipulate this problem. Using manipulatives maybe more helpful for some students who need the experience of physically manipulating an object to correctly solve the problem. Mathwire. (2010). Retrieved November 10, 2012, from