Analyzing+Concepts

**__Missing Number Problems - Introduction to Algebra__**

Alabama Course of Study: Math 10.) Complete addition and subtraction number sentences with a missing addend or subtrahend.• Applying commutative, associative, and identity properties of addition to solve problems • Identifying a rule when given a pattern involving addition or subtraction Lesson Objective**: By the end of the lesson students will be able to solve a missing addend problem where one addend and the sum is given by using pencil, paper, or counters.
 * Missing Addend: Number + N = Sum


 * Big Idea**: Addition problems can be solved when one of the addends have been omitted from the sentence. Problems like these can be solved in a variety of ways.


 * Teacher's Comment**:
 * I have noticed that the concept of completing an addition or subtraction problem with one of the addends or subtrahends missing is a skill that many students often struggle with. Taking away an essential part of the problem can throw off a student's understanding of the most basic operations if the skill has been taught with only one way to solve. Often this skill has been a matter of "you either get it or you don't" There is no "kind-of got it". This page will identify strategies for teaching the concept that will be helpful to learners of all abilities so that all students will "get it".

DISCLAIMER: I am using the 4th grade ACOS standard as a reference for this differentiation concept. Many of the examples I gave are much more basic than any 4th grader would really use. However, the most basic is a good place to start because even the slowest learner is able to not feel lost the entire time. Being the skilled teachers that we all are, we can use the examples I gave, and modify them to match the skill level of the students we are teaching. Naturally, if you are teaching a small group of gifted students, you won't use the 4+_=8 examples, and conversely with your slower learners, you wouldn't start out with +36=114. The videos are good for most students because they will pay more attention to a video and they begin low and then you can add more difficult problems as the lessons progress after the skill has been mastered.


 * Ways to Differentiate the Skill**:

Since this is a skill that can be difficult, a teacher needs to be prepared to present and teach the skill in a variety of ways. Perhaps students struggle with missing number problems because they have not been taught how to solve them in a way that they understand.

**Basic Whole/Small Group Lessons:

Auditory Learner Lesson**: Start with the basics to review the skills for slower learners. At the fourth grade level, these problems look like this: 47 + n = 98. Start small. To introduce the lesson so that slower learners don't feel overwhelmed from the beginning, give the problem 4 + n = 9. Ask students to explain how to find n. Gradually progress to larger numbers, 14 + n = 25, 24 + n = 50, and so on.

**Visual Learners**: Once again, start small. Draw a picture on the board, or if you're in a small group, demonstrate with counters. Show 4 circles. Tell them that you need 9 in all. How many more do you need to add to 4 to have nine? This shows them that they can draw a picture and count up from 4 to nine. Continue with gradually more difficult examples.

**Bodily/Kinesthetic Learners**: Pass out unifix cubes or small counter pieces. Have students make a stack of 4 counters. Tell them that we want them to end up with 9 counters. How many more do we need to add? Demonstrate that they can move 5 more counters to the stack to make 9. Repeat with a few more small number examples and then see if you are able to progress to more difficult problems.

**Working Backwards** : (I have noticed this works well with either low or high ability students. It seems to be personal preference.) Whether students can see and hear the problem and complete it, draw a picture or use counters, have them start with the sum. Write the problem 4 + n= 9 on the board. Explain that with addition problems you can work backwards. Begin with 9 (draw the pictures, use the counters). If you end up with nine, and they have given you 4 (have them separate 4 of the 9) how many more did they add to the 4? They should be able to see the other 5. Do this a few times. It shows that these problems can be solved by using the inverse operation- subtraction.


 * Web Resources for Differentiation:**

Here is a list of videos, podcasts and websites that offer good lesson plans and demonstrations to aid in teaching this concept.

Mystery of the Missing Addend This video opens in youtube and is a funny way of teaching the very basic 4 + _ = 8. It shows how to solve the missing addend problems using subtraction and a little bit of basic algebra. Good for the visual/auditory learners. It is entertaining because it is filmed to be like a 1930s dark detective movie in black and white.

Matchbox Cars ProblemMatchbox Cars Answer These two videos go together. A teacher shows 3 cars with some more under a garage. She asks students to figure out how many must be in the garage to make a total of 6 altogether. The second video shows how to solve the problem. This is good for all learners because the kinesthetic learners can act the problem out along with the teacher on the video. The visual learners can write the problem down to solve, and the auditory learners can just watch and enjoy.

[] Great link. This is a presentation that demonstrates how to use subtraction to find the missing addend. This would be good for quicker learners who don't ned to sit through the lesson and go through many examples. They can watch the presentation and keep going. Students who need reinforcement can watch the video to remember how to solve the problem.

[] This is a good visual link. It shows bees and a hive. Some bees go in the hive, there were 11 bees with 5 still outside. How many went in the hive? Kinesthetic learners can use counters or cubes to work out the problem before they insert their answers.

[] Yes, this is a worksheet, but once students understand the concept, they will need practice. Students can use any method necessary to solve the problems.

Missing Number Games This is a link to another page on the Wiki that has more games and pages that can be used by students individually.

This series can be used for your quicker learners to use individually. It goes through the process in a few different ways to find the missing addends in more difficult problems. After your other students have mastered the easier skills, these can be used to expand the concept. Missing Addends with Hundreds- Part 1 [|**Missing Addends with Hundreds- Part 2**]
 * Podcasts for your more advanced learners:**

[|Input/Output Lesson] This is a lesson plan that uses input and output patterns to reinforce skills associated with missing addends.
 * Lesson Plans**:

[|**Number Clues**] This lesson would be better for your more advanced students. Students use a set of clues to determine which numbers are missing and complete the various problems and number sentences.