The Arizona STEM Acceleration Project
Expanded Form of Numbers
Expanded Form of Numbers
A 2nd grade STEM lesson
Shonda Roer
1/29/24
Notes for teachers
In this lesson we will be representing numbers in expanded form and base ten numerals.
List of Materials
Math Standards
2.NBT.A.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:
2.NBT.A.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
Technology Standards
2.CS.D.1
Recognize that users have different needs and preferences for technology they used by selecting and operating appropriate devices. People use computing devices to perform a variety of tasks accurately and quickly. Students should be able to select the appropriate app/program to use for tasks they are required to complete. For example, if students are asked to draw a picture, they should be able to open and use a drawing app/program to complete this task, or if they are asked to create a presentation, they should be able to open and use presentation software. In addition, with teacher guidance, students should identify and discuss preferences for software with the same primary functionality.
Objective:
I can read, write and represent 3 digit numbers.
Agenda
**Full Lesson about 90 minutes
Intro/Driving Question/Opening
The students will answer some true or false questions to find any insights the students have of value of the digits in a three digit number. This should help the students to understand that numbers can be represented in many ways. The students will be looking at the value of each digit to decide if the equation is true.
True or False? Be prepared to explain.
True or False? Be prepared to explain.
c. 248 = 38 + 10 + 200
d. 604 = 40 + 600
What is different about the equation on problem c?
Hands-on Activity Instructions
This activity is supposed to help the students understand that when a number is written as the value of its digits it is expanded form.
The students will be writing the value of base ten diagrams in expanded form and as a three digit number. They will use https://app.kpmathematics.com/ to virtually represent the numbers.
I would copy slides 11-15 and 18-20 into their own slide presentation and then put it into google classroom for the students.
They can then put their answers on their slides. If you make a copy for each student then they can put their answers into it.
I would put the students into groups of 2-3.
I usually use flippity net to put them into random groups.
Activity synthesis: Ask the students “ What is the value of 40 + 200 + 7? Explain how you know.”
Aubrey has 4 hundreds. Jeffrey has 5 tens. Ava has 6 ones. They want to represent the amount they have using an equation.
Problem 1
Write an expression to represent the sum of their values.
________ + ________ + _________
Write the total value as a three digit number?
_______________
Write each number as the sum of hundreds, tens, and ones, and as a three digit number.
Problem 2
Expanded Form:
_____________________________
Three digit number:
_______________
Write each number as the sum of hundreds, tens, and ones, and as a three digit number.
Problem 3
Expanded Form:
_____________________________
Three digit number:
_______________
Write each number as the sum of hundreds, tens, and ones, and as a three digit number.
Problem 4
Expanded Form:
_____________________________
Three digit number:
_______________
Write each number as the sum of hundreds, tens, and ones, and as a three digit number.
Problem 5
Expanded Form:
_____________________________
Three digit number:
_______________
What is the value of 40 + 200 + 7? Explain how you know.
Activity Synthesis:
Hands-on Activity 2 Instructions
In this activity the students will represent numbers as a three digit number and in expanded form.
They will work with a partner and roll three dice. They will make a three digit number that matches the directions for each problem.
Roll the dice and make the largest number possible.
Activity 2 Problem 1
Write the three digit number:
_____________________________
Expanded Form:
_______________________________________
Roll the dice and make the smallest number possible.
Activity 2 Problem 2
Write the three digit number:
_____________________________
Expanded Form:
_______________________________________
Roll the dice and using the same digits make a number different than your partner’s.
Activity 2 Problem 3
Write the three digit number:
_____________________________
Expanded Form:
_______________________________________
What is the largest number you made?
How did you know if you were making the largest number possible?
Activity 2 Synthesis
Assessment
At this time, I would have the students do an exit ticket to show their understanding of the skills done in class today.
For exit tickets, present the problem on the board and have students complete their work on a note card, or half sheet of paper and turn in.
Assessment
Represent the number 425 as the sum of hundreds, tens and ones.
Expanded Form:_______________________________________________
Represent 200 + 60 + 7 as a three digit number.
Three digit number:____________________________________________
Differentiation
Remediation
Extension/Enrichment