Classroom Activities
In this section, I present three lesson samples used to teach place value in addition and subtraction. Each lesson is designed to emphasize one of the 3 models discussed above, "concrete", "pictorial", and "symbolic". Each also demonstrates a different sub-step of 2 digit addition and subtraction. I have also provided a list of word problems used throughout the year.
Activity 1
This activity demonstrates the concrete model, and will be used as a math starter activity for our daily math time. We will be using daily word problems for this activity. Students work in pairs using base 10 blocks to concretely workout the problem. This activity would supplement the sub-step above, on addition and subtraction with a single digit number and a 2 digit number, and covers the following Common Core Standards; 2.1OA, 2.2OA, 2.1NBT, 2.3NBT, 2.5NBT, 2.6NBT, 2.7NBT, 2.9NBT.
This activity will begin with the following word problem on the board. "There were 35 cubes in the tub. Timmy was cleaning up and found 4 more cubes and put them in the tub. How many cubes are in the tub now?" Students will gather their pre-assigned tub (during this unit of study each tub will contain 99 cubes, number cards 1 to 9 and 10 to 90, white board and white board markers) from the shelf and recreate this problem. They will need to be able to explain to the rest of the class each step they took to re-create the problem and share their reasoning. Each group who would like to share will have that opportunity. Even if each group took the exact same steps they are continuing to model for peers who may still be struggling with this concept while gaining the deeper more automatic understanding of how to problem solve.
Lesson Extension - Students will then be asked to use these same amounts of cubes 35, 4, and 39 and create their own subtraction story. Each group will have the chance to share their story with the class. This sharing of ideas will allow students to hear from other students the ideas we have been exploring and inspire them to think combining these numbers in multiple ways. Students are by this time in the year comfortable with multiple forms of the 14 possible word problems as outlined in the Common Core Standards and a variety of stories should develop.
Activity 2
This activity demonstrates the pictorial model, and will give students the opportunity for independent practice. Students will create word problems using place value cards to solve the problem, and will be given time to present their problem solving skills to the class. This activity demonstrates the sub-step above involving addition/subtraction of 2 digit numbers and multiples of 10 and covers the following Common Core Standards; 2.1OA, 2.2OA, 2.1NBT, 2.3NBT, 2.5NBT, 2.6NBT, 2.7NBT, 2.9NBT.
Students have access to their personal place value cards 10 – 90, and half a sheet of poster paper. Using the poster paper students will write one of the word problems they have created using the place value cards. This lesson will be independent practice; student will be assessed for understanding of concept. Their work will be displayed on our math wall. Students will be asked to use their tens place value cards to help them create a word problem. (Because they only have one of each and no 100 card the problem will not require regrouping) Student will be asked to show me the number cards they are using so I can assess weather or not they used correct number bonds. Students will then create an addition or subtraction story using their numbers. However, I will remind them they need to leave one of the numbers out of their story so that other students will have the opportunity to discover the missing number for themselves.
Lesson Extensions - These problems can be used during our daily word problem activity or as independent or pair working group activities during center time.
Activity 3
This activity demonstrates the symbolic model, and is used in a whole group setting as a guided practice. Students will use the expanded form and correct mathematical symbols to find the answer to problems. This activity also demonstrates sub-step 5 Regrouping with 2 digit numbers and covers the following common core standards; 2.1OA, 2.2OA, 2.1NBT, 2.3NBT, 2.5NBT, 2.6NBT, 2.7NBT, 2.9NBT.
I will use this as one of the first symbolic model activities within this particular sub-step. As a class we will work the following problem out on the smart board: 35+27 = ? I will write this problem on the board and ask various students to help write out the next step. The first step will be to write it out in expanded form 30 + 5 + 20 + 7. I will ask them what to do next. The next step will be to group like numbers (30 + 20) + (5 + 7). At this point some of the students may want to combine the 10's so we are left with 50 + (5 + 7). It is now necessary to break apart a number in order to add the remaining 5+7. This could be breaking the 5 into 2 and 3, then combining 3 with 7 to make 10, or it could be breaking the 7 into 2 and 5, then combining the 5's to make 10. Both ways are correct and we will write them both on the board and discuss how in the end they will both work to give us the right answer. These methods are illustrated by the following:
50 + 5 + 7 = 50 + (2 + 3) + 7 = 50 + 2 + (3 + 7) = 50 + 2 + 10 = 60 + 2 = 62
50 + 5 + 7 = 50 + 5 + (5 + 2) = 50 + (5 +5) + 2 = 50 + 10 + 2 = 60 + 2 = 62.
This is the format that we have been and will continue to work with until students can show mastery.
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