Unit 1 Number Relationships (Additive Thinking)

Unit Driving Question 

How can we use addition strategies to solve real world problems? 

Essential Questions 

1. How can we represent numbers in different ways?

2. What relationships do we find in mathematics?

3. How do we apply addition and subtraction strategies when problem-solving?

4. How do we use properties of addition?

Big Ideas 

1. Numbers have value that can be represented in different ways

2. Flexible methods of addition and subtraction computation involve taking apart (decomposing) and combining (composing) numbers in a wide variety of ways.

3. The commutative, associative, and identity properties are used to find equivalent expressions.

4. Number relationships determine the pattern, rule, or unknown number.

5. Estimation is a problem-solving strategy when finding sums and differences of numbers. 

Technology Resources 

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.

• Third Grade List- This list has resources that can be used all year long.

Resources Within This Unit

• Big Idea 3:

• XL Practice Game: This is an online game you can play with your students to practice identifying the properties of addition. This is a song on Youtube that helps students learn the properties as well.

• Big Idea 4:

• Function Machine Game: This is a great whole group activity to do with your class.  Choose the machine and type a number in the “input” box. Students figure out the rule based on the output. The class can keep putting new inputs in until they figure out the rule.

• Some other practice websites you can use to practice the skills in this big idea: Pattern Generator, What Comes Next, Geo Patterns, and Numbers & Arithmetic Math Problems

Additional Resources

• Place Value Hockey- ABCYa game that allows students to practice place value at various levels.

• Pet Bingo- This app can start being used in Unit 1 and continued into Unit 2. They can practice all four operations or mix them up altogether.

Launch Task 

1 Lesson 

Big Ideas for Development Lessons 

5-6 Weeks

Big Idea 1: Numbers have a value that can be represented in different ways.

Collaborative Engagement 

1. Place Value Sort: Students sort different representations of a number and create a visual representation using place value blocks or other manipulatives.

Key Resources 

1. Place Value Challenge: Give each student a 4, 5, or 6 digit number (depending on progress/level of student). Tell them they have 5 minutes to come up with as many ways to represent that number. They will most likely write the number in standard, written, expanded, and model form first. Prompt students to think outside the box. If students are struggling, show an example of a stand out student. For example, Emily has the number 1,598. Instead of using 1 thousand and five hundreds blocks, she may have thought to use 15 hundreds blocks. After five minutes, have students share some of their examples. Give students a chance to go back and reevaluate their number and see if they can come up with other ways to represent it. This could be a follow-up activity: More Than One Way.
2. More or Less This game can be played in small groups, as a whole group, or in teams. Students give each other five digit numbers (can do this with four digit numbers as well, but do not give the +10,000 or -10,000 card) and then another student pulls one of the cards. They then have to figure out the number. For example, Sally gives the number 15,982. Her partner pulls the card -10,000. If his answer is correct (5,982), his partner Sally will say “I agree because…” or if his answer is incorrect (ex: 14,982), his partner will say “I disagree because…” If you wanted to introduce as a class, the teacher would give a number and then pull one of the cards. The class would write their answers on whiteboards and then go through the answers that were given. If you wanted a grade, you could use the recording sheet. For a challenge, you could fill out the bottom cards with numbers like +20, -50, etc.
3.  Number Card Activity Comparing/Ordering: Give students four single-digit cards. Have students organize the numbers in any way that makes sense to them. They may order their numbers from least to greatest or greatest to least (ex: 1,478 or 8,741) or organize them by odd or even (ex: 1,748) or another reason that makes sense to them. Have students share how and why they organized the digits in the way that they did. Once students have the opportunity to share, have them turn to their partner and look at each other’s numbers. Have students compare and contrast their two numbers, and record their findings in any way they choose. Monitor the room as they create their list, Venn diagram, etc. Have students share their findings (ex: one student has a 3 in the thousand place and the other has a one). With this in mind, have them consider which number is greater. Have students explain how they know. Model how to compare those numbers using symbols. Continue the task using five digit numbers as well. Number Cards link  Comparing Numbers Task

Big Idea Formative Assessment 

1. Place Value - More or Less: An assessment that can be used at towards the end of big idea 1 instruction. 

Evidence of Understanding 

Represent numbers in multiple modes, including verbally, written form,  models, standard and nonstandard form.

• The standard form is the number written in digits.

• The model form can be represented by base ten manipulatives and pictures or in a chart.

• The nonstandard form includes expanded form and other decomposed expressions.

• Written form describes number using words.

Compare the value of numbers to determine how they relate to one another.

• Each place within the number has a value that is important.

Order multiple numbers based on their understanding of place value.

• Numbers can be arranged in ascending (least to greatest) or descending (greatest to least) order.

Big Idea 2: Flexible methods of addition and subtraction computation involving taking apart (decomposing) and combining (composing) numbers in a variety of ways.

Collaborative Engagement 

1. Prove it Challenge: Give students an addition problem on the board (example: 259+164). Tell the students they have to figure the answer without regrouping. They can use base ten blocks, number lines, etc. Prompt students through the process and share the different strategies students came up with.

Key Resources 

1. Flexible Strategies for Addition and Subtraction: This is more of a teacher resource than an activity for the students. For teachers who are unfamiliar with the different strategies or could use a refresher, this is a great resource for you! This is another source you can refer to.
2. Problem Solving Visuals: This is another great visual to use to help students understand the difference between addition and subtraction. It also includes example word problems for students to answer.
3. Compatible Numbers (Finding Sums): This task challenges students to find sums based on a game board given to them by their teacher. Adapted from North Carolina 3-5 Formative Instructional and Assessment Task Here is another resource students can use to help them through the problem-solving process.

Big Idea Formative Assessment 

1. Travel Through Europe: This is a higher level problem that students need to apply the strategies they have learned throughout this unit.

Evidence of Understanding 

Add and subtract multi-digit numbers using a variety of strategies to compose and decompose numbers.

• Compose and decompose numbers based on their understanding of place value.

• Addition is the combination of numbers and subtraction is the separation of numbers.

• Place value models represent the relationship between numbers when regrouping.

Justify solutions using the inverse operation when problem-solving.

• Addition and subtraction are related as inverse operations.

Big Idea 3: The Commutative, associative, and identity properties are used to find equivalent expressions.

Collaborative Engagement 

Balancing Equations:

Students use scales to check if equations are “balanced” or equal to one another.

Examples of equations:

4+8=12

8+2=2+8

9+(3+4)=4+(9+3)

Key Resources 

1. XL Practice Game: This is an online game you can play with your students to practice identifying the properties of addition. This is a song on Youtube that helps students learn the properties as well.
2. Ginger Snaps Properties of Addition Tips & Activity: This website gives some helpful tips and a dice activity students can do to practice the different properties.

3. Active Addition Properties: The scale activity will work well for visual learners to see how they are “balanced” on both sides. This is an activity you can do to get students out of their seat and visualize the properties. Give students different numbers of items (example: Person One- 7 marbles, Person Two- 4 marbles); have the students figure how many they have total. Then have the students switch positions (example: Person Two- 4 marbles, Person One- 7 marbles). Ask the students if they still have the same amount of marbles.

Big Idea Formative Assessment 

1. Mix, Match, Freeze: This is a free resource from Teachers Pay Teachers that you can use as a review game. Then you can give the students the quiz at the end as a formative (or summative) assessment.   

Evidence of Understanding 

Apply properties to form a conceptual understanding of equivalent expressions.

• Flexible methods for computation require a deep understanding of the operations and properties of operations.

Big Idea 4: Number relationships determine the pattern, rule or unknown number. 

Collaborative Engagement 

1. Cinema Disaster This is a problem that students can work on that will activate their knowledge of pattern that they can solve by drawing pictures, making a table, using manipulatives, etc.

Key Resources 

1. Geometric Patterns: Activate prior knowledge of patterns by giving students different patterns including shapes. Discuss different situations or solutions depending on the problem. Have students partner up students create patterns of their own using manipulatives. Their partner can then guess the partner or predict what steps would come next. 
2. Number Patterns: This is a free resource on Super Teacher that has students analyze a number pattern and explain which numbers come next and why.
3. Function Machine Game: This is a great whole group activity to do with your class.  Choose the machine and type a number in the “input” box. Students figure out the rule based on the output. The class can keep putting new inputs in until they figure out the rule.
4.  Function Machine Graphic: To teach function machines, you can use the following graphic on SMARTboard and write the numbers that go in and out. You can also give them the input or output with the rule and have them figure out the other number.
5. What’s My Rule? Draw an input and output table on the board. Tell students they will be guessing the rule based on the numbers’ relationship. When students figure out the rule, they raise their hand but do not shout out the answer. They keep adding numbers until all the students are confident of the rule. Then we share and show why that is the rule.
6. Input/Output Task Cards: Before independent practice, make sure to discuss the importance of the rule fitting each row of the table. Rules can sometimes be deceiving! 
7. Here are some other practice websites you can use to practice the skills in this big idea: Pattern Generator, What Comes Next, Geo Patterns, and Numbers & Arithematic Math Problems

Big Idea Formative Assessment 

1. Representing the Problem: Students determine whether an equation fits a given word problem. They have to reason why or why not as well.

Evidence of Understanding 

Determine the pattern based on how the numbers relate to each other.

• Patterns can grow or shrink based on the rule.

• Patterns recur in multiple mathematical concepts.

• Patterns can consist of geometric shapes, numbers, and pictures.

Analyze the numbers given in an input/output relationship to determine the rule and find missing values.

• The value of numbers and how they relate to one another can help determine the rule or unknown number. 

• Problem-solving strategies for addition, subtraction, and multiplication provides guidance when analyzing input/output tables, function machines, and patterns.

Big Idea 5: Estimation is a problem-solving strategy when finding sums and differences of numbers. 

Collaborative Engagement 

1. Number Line Bingo: Students fill out their bingo card with rounded numbers. A list of example can be presented on the board. Students mark the rounded number on their bingo board using a number line. Example:  Teacher call the number 74. Students fill out their number line from 70 or 80 and mark 74 on the number line. They then evaluate if it is closer to 70 or 80. They then mark the number on their bingo card.  

Key Resources 

1. Place Value Web: This assesses their place value knowledge and their understanding of rounding.

2. Three Digit Rounding Bingo: This is similar to the collaborative engagement, but it bumps up the rigor. Students fill out their bingo boards with any three digit number. The teacher calls out the rounded number. If the students have a number that rounds to the number called, they can mark it. Example: Susie has 624 on her board. The teacher calls out 600. Susie can mark her square since 624 rounds to 600 when rounding to the nearest hundred.

3. Estimating Heights: Students have to evaluate the logic of two boys who are measuring their height and drawing conclusions based on estimations. Adapted from North Carolina 3-5 Formative Instructional and Assessment Task.

Big Idea Formative Assessment 

1. Cafeteria Lunch Order Rounding Adapted from North Carolina 3-5 Formative Instructional and Assessment Task

Evidence of Understanding 

Add and subtract rounded numbers to solve real world problems.

• Estimations are important when the exact number is not needed.

• Compatible numbers guide students to find reasonable estimations.

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment)  

• Skeeball Machine Activity: The initial task was adjusted to be more vigorous and thought-provoking.