T4T Compare, Difference Unknown

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Lesson excerpt:

NC Mathematics Standard(s):

Represent and solve problems.

NC.1.OA.1 Represent and solve addition and subtraction word problems, within 20, with unknowns in all positions, by using objects, drawings, and equations with a symbol for the unknown number to represent the problem, when solving:

● Add to/Take from-Change Unknown

● Put together/Take Apart-Addend Unknown

● Compare-Difference Unknown


Additional/Supporting Standard(s):

Add and subtract within 20.

NC.1.OA.6 Add and subtract, within 20, using strategies such as:

● Counting on

● Making ten

● Decomposing a number leading to a ten

● Using the relationship between addition and subtraction

● Creating equivalent but easier or known sums.


Use place value understanding and properties of operations.

NC.1.NBT.5 Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.


Standards for Mathematical Practice:

1.   Make sense of problems and persevere in solving them.

3.      Construct viable arguments and critique the reasoning of others.

4.      Model with mathematics.

5.      Use appropriate tools strategically.

6.      Attend to precision.


Student Outcomes:

·       I can use addition and subtraction to solve problems within 20.

·       I can decompose a number leading to a 10.

·       I can mentally find 10 more and/or 10 less than a number and explain my reasoning.

·       I can justify the reasonableness of my answer and explain my strategies.



·       Word problem on chart paper to use with whole group

·       A class set of printed copies of the problem for students to glue in their math journals

·       Paper or math journals for recording solutions

·       Baskets of tools for each table or for groups of students to share. These should include various problem-solving manipulatives such as two colored counters, snap cubes, beans, hundreds boards, or number lines


Advance Preparation:

·       Review the significant ideas in Critical Areas 1 and 2 for First Grade to connect this lesson with key mathematical ideas of developing an understanding of addition and subtraction and number relationships.

·       Prepare baskets of materials, including only materials which have been introduced and used in previous lessons.

·       Prepare a written copy of problem on chart paper.

·       Prepare a class set of the problem for individuals.


1.      Gather students on the floor.

2.      Show students the following problem on the chart paper, asking them to read aloud with you. Read again.


Sam has 6 books. Joe has 16 books. How many more does Joe have than Sam?


3.      Ask students to restate the problem in their own words. Students “unpack” the problem (give the information they know about the problem from reading it. See the guiding question suggestions in the “before the lesson” question section below).

4.      Send students to their work spaces to glue a personal copy of the problem in their journals or on a piece of paper.

5.      Have students solve the problem with manipulatives, words, and/or pictures.

6.      Students should add an equation to match their solution.

7.      Record their solution strategies and equations in their journals.

8.      While students work, the teacher observes and asks questions, recording student responses. (The teacher also decides which students will share their solution strategies with the group.)

9.      Bring the students back together as a group for sharing. It is important for the teacher to allow students to do most of the talking and questioning, with teacher offering support and clarification if needed.


Questions to Pose:

While students are in whole group:

·             What do you know about this problem?

·             Tell me in your own words.

·             What are some ways you can show your mathematical thinking when you work on this problem?

As they work on the problem:

·       Tell me about your thinking.

·       What does this part of your solution show?

·       Reread the problem again for me. What is the problem asking you to find?

·       What tool did you decide to use for this problem? Why did you select it?

·       What would happen if …? (Pose situations to extend their thinking such as, if you wanted Joe and Sam to have the same number of books, what might you do?)

·       How can you show that solution on paper for others to see? How can you solve that problem mentally?

·       How can you represent this problem in another way?


After solving (whole group):

·       Who can restate what our problem was asking us to find?

·       Tell the group how you solved it? What did you do first? Why? What did you do next? Why?

·       What was your mathematical thinking for this problem?

Possible Misconceptions/Suggestions:

Possible Misconceptions


Student adds the two known numbers.

Ask the student to reread and “unpack” the problem, noting the problem structure.

Have the student represent Joe’s set with cubes and then Sam’s set with cubes.

Ask the student to tell what the problem is asking us to find out.

Discuss the reasonableness of the student’s original response when comparing the two sets.

Special Notes:

Make notes as you observe students working to determine who will share with the group. Decide the sharing order for selected students beginning with a student who has a simple solution and progressing to students with more complex solution strategies. This allows students to visualize connections and relationships in solution strategies.


This problem is an example of the problem structure, Compare-Difference Unknown. Teachers should be aware that some students may solve this problem using subtraction or addition, but some students will solve mentally finding 10 more /less, or by decomposing numbers. A student who solves this way might respond, “I just knew it in my head! I knew that 16 is ten more than 6 so my answer is 10”, or “I know doubles, so I know that 6+6=12 and it takes 4 more added to 12 to make 16, so I know 6+4=10, so my answer is 10.”


To extend this problem ask students how they might change this problem to tell about Sam’s books, making this problem a “How many fewer?” version of a Compare Difference Unknown problem. (See Table of Common Addition and Subtraction Situations).

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