1st Grade Unit 4: Problem Solving Builds Number Sense 

Unit Driving Question 

How do we develop an understanding of whole number relationships?  

Essential Questions 

1. How does adding and subtracting help me problem solve and build number sense?

2. How do number relationships help me problem solve and build number sense?

3. How can patterns in math help me problem solve and build number sense?

4. What are other solutions to this problem?

Big Ideas 

1. Problems can be solved flexibly, efficiently, and accurately.
2. Addition and subtraction are related.
3. Addition and subtraction follow patterns.
4. Unknown numbers can be identified using relationships of numbers. 

The following apps, websites, and smartboard lessons can be used throughout the unit, as needed, during small groups, lessons, to reinforce standards.  They are also useful for students who may need reinforcement, remediation, or differentiation. 

http://www.sheppardsoftware.com/mathgames/matching/AdditionX.htm -addition

https://www.nasa.gov/kidsclub/flash/games/level3/Blast_Off.html#.UmgLgfmkoiY -addition

https://www.arcademics.com/games/jet-ski- addition

https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Oktas-Rescue/- addition

http://www.ictgames.com/dinosaurDentist/index.html- Adding and subtracting

http://www.abcya.com/subtraction_game.htm- subtraction

http://www.abcya.com/math_stack.htm -subtraction

http://www.ictgames.com/octopus.html- 10 more

https://www.topmarks.co.uk/Flash.aspx?f=FunctionMachinev3- Function Machines

https://www.mathlearningcenter.org/resources/apps - Multiple manipulatives free and can be accessed by apps or website

Launch Task 

1 Lesson 

Big Ideas for Development Lessons 

4-5 Weeks (approximately 1-2 weeks per big idea) 

Big Idea 1: Problems can be solved flexibly, efficiently, and accurately. 

Collaborative Engagement 

1.  Review the animal book and pose the following activity:  The Oklahoma City Zoo will be receiving 16 new animals.  Some are zebras, some are chimpanzees, and some are giraffes.  How many of each kind could they be receiving?  Use any tools that you might know about, some examples might be, data tables to record your responses, part-part-whole mat, linking cubes, or ten frames and counters.  Answers will vary.

Key Resources

1. Kiri’s Mathematics Game - Students turn over 2 cards to try to get to the target number card by adding or subtracting.
2.  Addition and turn around fact activities with linking cubes:
1. Link Cube Addition 
2. Turn around trains 
3.  True or False -  Students look at math facts and determine if they are true or false.  

Big Idea Formative Assessment 

1. Questions:  Is there another combination of the zoo animals in the earlier lesson?  Have you found all of the possibilities?  How do you know?  How many more of animal A do you have in this table than animal B or C?  How did you know the total of each animal?  How does creating a table to help you determine your addends?  Students could be given a greater sum or amount of animals.  Students could write and solve their own story problem with three or more addends. 

Evidence of Understanding 

• Can solve problems flexibly, efficiently, and accurately determining if their answer is reasonable.

• Use number relationships to solve a problem.

• Can make connections between counting and the operations of adding and subtracting.

Big Idea 2: Addition and subtraction are related.

Collaborative Engagement 

Domino Addition and Subtraction

• Gather students and draw several dominos on the board. You can also make a large demonstration dominos by cutting a piece of poster paper in half and drawing dots on either side. Ask students to look at both halves of the domino and tell how many dots are in each square.  

• Some questions might be:  What is the sum if you add the dots in each square?  Will the sum change if I flip the domino (180-degree turn)? Why do you think this? (Special Note: This is not about students understanding degrees and angles. It is included for teachers to identify the specific way to flip the domino.)   Is there another way we could write the addition sentence and still get the same sum?  What would the difference be if you subtracted the number of dots in one of the squares from the sum?  What type of relationship are you noticing?  What are the number sentences in the fact family for this domino?

• Allow children to work independently to record the fact families that their dominos show. They will need to draw each domino and label it with their fact family using the recording sheet.

• Observe the counting strategies that the children utilize. Notice if they are counting on, counting each individual dot, or recalling the answers because they know their addition and subtraction facts. (Note: Students are only being exposed to the concepts of vertical and horizontal. It is not the focus of the task, but teachers are encouraged to use the vocabulary terms. Students are not responsible for this yet.)

• Allow several students to share their work. Allow students to discuss how they determined the number sentences in their fact family and the strategies they used to create these number sentences. 

Key Resources 

1. Domino Addition - Students explore the commutative property with dominoes.  
1. https://www.illustrativemathematics.org/content-standards/1/OA/B/3/tasks/1219 
2. http://www.makinglearningfun.com/themepages/MathDomino.htm  
2. Fact Families- Using three cards students will find math facts that relate to all three numbers
3. Fact Families with Picture - Students look at dot pictures and write related addition and subtraction facts to go with each one
4. Students will play Ten Wins! with a partner.   

• Each player will need 10 counters of one color.

• Player one will roll the dice and add the two numbers to find the sum. Cover the sum with their designated color counter.

• Player two will roll the dice and add the two numbers to find the sum. They will also cover the sum with their designated color counter.

• If space is already covered by the opponent’s counter, then a player may steal that spot. Example: Player one has a blue counter on the number 9. Player two rolls a 5 and 4. Player two may remove the blue counter and place their color counter on that space.

• The first player to use all ten counters on the game board wins!

Big Idea Formative Assessment 

• Give students note cards that have an addition or subtraction number sentence written on each card. Have students group the cards into fact families.

• Once they get the hang of this, give them three of the four number sentences and they have to figure out the one that is missing.

• As they get better with the game start decreasing the number of sentences you give them.

• Once they can tell you three of the sentences when you have only given them one, change the game.

• You give them all the number sentences in the family and they have to tell you who the individual family members are.

Evidence of Understanding

• Can solve problems flexibly, efficiently, and accurately determining if their answer is reasonable.

• Use number relationships to solve a problem.

• Can identify and create fact families using related numbers efficiently to add and subtract.
   

Big Idea 3: Addition and subtraction follow patterns

Collaborative Engagement 

• Read - Animals on Board by Stuart Murphy or another animal book before the lesson.
• Vocabulary - addition, subtraction, fact family, difference, sum, plus, minus (can make an anchor chart)
• Counting - Before reading it to the class,  put post-it notes over the equations and have the kids try to formulate it on their own (using whiteboards at the rug), then remove the post its to reveal the answer. That gives all the kids a chance to think about the addition story problem being presented and do the math themselves.
• Using Complete Sentences - Allow students to make their own page for the book with illustrations and a sentence using the book as a model.
• Setting a Challenge - Roll dice, use dominoes, or draw number cards to make addition sentences, find a sum with a classmate or by themselves.
• Read for Subtraction - If You Were a Minus Sign by Trisha Speed Shaskan
• Wrapping Up - Allow students to practice fact families and then build their own.

Key Resources 

1. Guess my Rule - students will find common patterns to discover a mathematical rule.
1. http://mathwire.com/games/guessmyrulegame.pdf
2. http://thinkmath.edc.org/resource/guess-my-rule 
2. Finding Patterns  -using a blank hundred chart allow students to find patterns and highlight them, students can highlight patterns that they know and explore patterns they might discover as they work. Allow students to share patterns on the overhead, Smartboard, or at whole group time.  The student should be able to name the pattern with a sentence starter such as; I found a pattern that (adds or subtracts) __ each time, they should also be able to explain and model the pattern for the class. 

Big Idea Formative Assessment 

1. Use the Finding Patterns lesson to assess students understanding of patterns.  They should be able to find, model, extend, share, and explain their patterns using the appropriate vocabulary.

Evidence of Understanding  

• Can solve problems flexibly, efficiently, and accurately determining if their answer is reasonable.

• Can identify and use patterns when adding and subtracting.

• Can flexibly use strategies to add and subtract such as doubles, making ten, etc...

Big Idea 4: Unknown numbers can be identified using relationships of numbers. 

Collaborative Engagement 

Missing Addends Activity -

• Introduce missing addend by place 6 cars around the room hidden, but that can be easily found.  

• The teacher may write the problem on the board or project the problem.  I had 8 toy cars at my desk, but now I only have 2 cars. I need to find out how many cars are missing.  

• Write the subtraction sentence on the board 8-2=?.  Think-aloud:  Now I have 2 toy cars and some toy cars are missing. I will write 2 plus some cars = the 8 cars that I know I had to start with, 2+? =8

• Ask students why they think you wrote a question mark instead of a number in the equation. Students should respond with that is the amount we do not know.  

• Invite six students to locate the cars. Each student will take a turn to locate one car. The other students are sitting in their seats. They may tell their classmates using soft voices if they see a car.  As the cars are found write the numbers of cars found on the board.

• Ask students: How can we check if we found all the cars? Ask students: What information in this situation do we know that will help us find the missing (amount) addend?

• Set up the problem on a part-part-whole mat and then ask students:  If I had 2 cars and we had to find some more to get to 8, how would I could I draw this on my mat?  

• The teacher will write students response in the Part, Part, and Whole Box on the board.  Explain: The missing number is my missing addend. Addends are two parts of a whole.

• Allow students to use linking cubes to create their own missing addend problems.

Key Resources 

1. Part-Part-Whole Cards - Students use cards to find the missing part (number) from the whole.
2. Cave Game Subtraction - Students will hide part of a whole in their cave for classmates to figure out how many are hidden.
3. Find the Missing Number - Students will try to use number cards to find the correct missing numbers in  equations.
4.  Take From - Word problems involving subtraction with the change unknown 

Big Idea Formative Assessment

• Draw objects of two given numbers. For example, draw 2 soccer balls, and then draw 5 soccer balls.  Ask students:  Are the objects are one whole group? If so, why? If not, why?

• Then ask: How can we make a whole group of soccer balls?  Draw a new picture to represent the whole group.

• The teacher will draw a part-part-whole box on the board. Ask students to help you complete the box using the numbers 2 and 5.  

• Ask students: What are the parts and what is the whole they make?  After passing out counters, explain to students they will make the numbers 3 and 4. (Use Part-Part-Whole Mat) a) Observe students creating and identifying the two different addends using counters. Walk around the room and ask: b) What two parts do you see? 2) Tell: Put the two parts together.  

• Ask: What whole number did you make? Students should be able to say 7. a) Observe students using counters by putting the two separate parts (addends) together.  

• Make a note of who might have trouble with this activity. 3) During the independent activity: Students will demonstrate their understanding of finding the missing addend when writing an addition sentence with the missing addend.

• The student will write their matching subtraction sentence in Math Journals.

Evidence of Understanding 

• Can solve problems flexibly, efficiently, and accurately determining if their answer is reasonable.

• Use other numbers in the problem to identify unknown numbers based on knowledge of number patterns.

• Use flexible strategies to identify missing parts of a whole.

Unit Re-Engagement

Ongoing

Unit Re-Engagement: Students will create a story about their missing addend. Give students a format to follow for the writing. Example: I have 7 blue crayons. Robert has some more blue crayons. Altogether we have 13 crayons. How many crayons did Robert have?

I have______________.

(friends name) has some more________________.

Altogether we have________________________________________.

How many _____________________did (friends name)_____________have? ______.

(friends name) has some more________________.

Altogether we have________________________________________.

How many _____________________did (friends name)_____________have?