2nd Grade Unit 1: Developing Place Value and Base-Ten Concepts

Unit Driving Question

How does place value help us understand number relationships?

Essential Questions

1. What are ways we recognize mathematics in our world?

2. What relationships do we find in mathematics?

3. What are different ways to show numbers?

Big Ideas

1. Our number system is based on ten.

2. Numbers can be represented in many ways.

3. Place value helps compare and order numbers.

4. Compatible numbers aid in problem-solving.

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.

Base Ten Recognition Students can practice identifying base ten blocks, matching it to the standard form.

Virtual Base Ten Blocks

Addition Fluency Practice with logic Students have to choose addends to make a target number.

Number Bonds 40  Practice addition fluency to 40.

Addition Fluency Practice Students create determine the missing addend.

Thinking Blocks Addition and Subtraction Students use the part-part-whole model to practice problem-solving using addition and subtraction.

Minus Mission Students increase fluency with subtraction facts.

Virtual Number Line

Launch Task

1 Lesson

• Give a collection of objects (cubes, beans, counters, etc.) that number between 75 and 100 to every two students. Ask students to work with their partners to find out how many objects they have and to discuss how they found their answers. Select three pairs with different strategies to present their thinking to the class.  Lead a discussion as to why the strategies worked.

Big Ideas for Development Lessons

5-6 Weeks (approximately 1 1/2 weeks per big idea)

Big Idea 1: Our number system is based on ten.

Collaborative Engagement

1. Materials: Various materials, such as base-10 blocks (flats, longs, cubes), counters, pennies, ten-frames, craft sticks, paper and pencil, etc.
1. Instruct the class to work in groups to make the number 127 using any materials they choose. Choose groups to present and describe their representation to the class.
2. Ask students what their favorite representation is and why.
3. Instruct the class to work in groups to make the number 127 using base-10 blocks.
4. What are all of the ways to make 127?
5. How do you know you found them all?
6. Record your answers.
7. What is the least or most amount of ones you can use?
8. What is the least or most amount of tens you can use?
9. What if there were no flats? How would you make the number? 

Key Resources

1. Building & Busting Towers of 10 - game which uses base-10 blocks or Unifix cubes to reinforce place value, adapted from Georgia Department of Education
2. Boxes of Juice - a number story adapted from NC Department of Instruction (Task 3b)
3. Number Pieces App - This is an online base-10 block resource for interactive whiteboard. Students with fine motor challenges may also benefit.

Big Idea Formative Assessment

1. The Number 179- task adapted from NC Department of Instruction (Task 1c)

Evidence of Understanding

• use numerals, words, pictures, tally marks, number lines, and manipulatives to represent numbers up to 1,000

• 10 is ten ones (called a “ten”), 100 is ten tens (called a “hundred”), 1000 is ten hundreds (called a “thousand”)

• recognize the value of zero (0) as a digit

• demonstrate a variety of methods to find 10 more or 10 less and 100 more or 100 less, such as counting up or down, number line, and number grid 

Big Idea 2: Numbers can be represented in many ways.

Collaborative Engagement

1. Benchmark Collection Boxes
1. Students each draw 4 large rectangles on a piece of paper. Teacher tells students that the rectangle is a collection box that is used for collecting different names for numbers. For the first rectangle, students write the digit ‘10’ in the top corner of the rectangle. As a class, discuss names for the number ‘10’ (“ten”, ten tally marks, a dime, a ten-frame, etc.).
2. Next, in small groups, students will make collection boxes for numbers such as ‘15’, ‘25’, ‘45’, or other benchmark numbers. (Note: Using numbers which correlate with money (nickels-5, 10, 20; dimes-10, 20, 30, 40; or quarters-25, 50, 75) or time (quarter hour-15, 30, 45) will help prepare students for future units.) Compare and record answers.

Key Resources

1. The Number 247- task adapted from NC Department of Instruction (Task 1a)
2. Number Lines with Same Length but with Changing Numbers - exploration with open number lines from M4YC (click on the PDF icon)
3. Largest Possible Numbers -  place value task adapted from NC Department of Instruction (Task 1f)

Big Idea Formative Assessment

1. Exit ticket: Represent any 3-digit number in two ways, at least one of which uses base-10 blocks.

Evidence of Understanding

• use representations of whole numbers up to 1,000, such as numerals, words, pictures, tally marks, number lines, and manipulatives

• read whole numbers up to 1,000

• write whole numbers up to 1,000

• discuss whole numbers up to 1,000

• locate whole numbers up to 100 on an open number line 

Big Idea 3: Place value helps compare and order numbers.

Collaborative Engagement

1. Three on a Bench - comparison and ordering number story from New Zealand Ministry of Education

Key Resources

1. Close, Far, and In Between (adapted from Van de Walle, p. 197, Activity 11.21)
1. Put any three numbers on the board, such as 90, 175, 250 (Benchmark numbers up to 500 are suggested.).
2. With these three numbers as referents, ask questions such as the following, encouraging discussion of all responses:
1. Which two numbers are closest? How do you know?
2. Which number is closest to 300? To 500?
3. Name a number between 175 and 200.
4. Name a multiple of ten between 175 and 250.
5. Name a multiple of one hundred between 250 and 500.
6. Name a number that is more than all of these numbers.
7. About how far apart are 90 and 250?
8. If these are “big numbers,” what are some small numbers? Numbers that are about the same? Numbers that make these seem small?
2. What’s Your Number?
1. Materials: 3 dice, recording sheet
2. Roll the 3 dice.
3. Arrange all three in order to make 6 different numbers. e.g. 3 2 6 326, 263, 632, 362, 236, 623.
4. Record your numbers as in the example above.
5. Order your numbers from least to greatest.
6. Show your numbers using various representations such as pictures, standard notation, and expanded form.

Big Idea Formative Assessment

1. Exit ticket: Place a given set of numbers, ranging from 0-1,000, in order.

Evidence of Understanding

• compare and order whole numbers up to 1,000

Big Idea 4: Compatible numbers aid in problem solving.

Collaborative Engagement

1. “I need to buy pencils for our class. If pencils come in packages of 10, how many packages will I need? Why? How many extra pencils will we have? What if I can buy packages of 5 and 10? How does your answer change?”

Key Resources

1. “Close, Far, and In Between (adapted from Van de Walle, p. 197, Activity 11.21)
1. Put a variety numbers on the board, such as 75, 89, 112, 137, 250, 415
2. With these numbers as referents, ask questions such as the following, encouraging discussion of all responses:
3. Which two numbers are closest? How do you know?
4. Which number is closest to 300? To 500?
5. Name a number that is more than all of these numbers.
6. About how far apart are 75 and 112? 250 and 415?
7. If these are “big numbers,” what are some small numbers? Numbers that are about the same? Numbers that make these seem small?
8. What numbers are close to 100? 200? 300? (Discuss patterns.)
2. Birthday Cupcakes - estimation number story from Balanced Mathematics Assessment, Harvard University Graduate School of Education ,Cambridge MA 

Big Idea Formative Assessment

1. Exit ticket: Given a number line from 100 to 200, marked with intervals of ten, students place a set of numbers (from 101-199)  to the closest 10 and the closest 100.

Evidence of Understanding

• use benchmark numbers as compatible numbers

• recognize when to round numbers to the nearest 10 and 100 

Unit Closure

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

1. Capturing Student Thinking - adapted from NC Department of Instruction (Tasks 3d and 3e) and intended for discussion and re-engagement, not as a worksheet.