10X Bigger!

By Amelia Terrapin, for Big Ideas in Beta

LEARNING OUTCOMES:

• Students will recognize that a digit in one place represents 10x the value of the digit to its right. 
• Students will be able to compare multi-digit numbers using <, =, > by looking at the value of the digits in each place. 
• Students will add and subtract multi-digit numbers. 
• Students will work cooperatively in groups to arrive at solutions.

COMMON CORE STANDARDS ADDRESSED:

Generalize place value understanding for multi-digit whole numbers.

• 4.NBT. 1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
• 4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
• 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

4.NBT.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

TIME REQUIRED FOR LESSON:

45 minutes to one hour

TIME REQUIRED FOR TEACHER PREPARATION:

Less than ten minutes

MATERIALS FOR LESSON:

• Index cards
• Pencils/pens
• 3 Poly spots, cones or other kind of marker for ones, tens and hundreds place
• Open space; push the desks aside, going to the gym or outside is ideal Teacher-created worksheets for recording unifix work; see step 5 of lesson overview

OVERVIEW OF LESSON:

1. Write a 3-digit whole number on the board, for example, 400.  Ask the students “Can anyone figure out how many tens are in this number?” Write a single digit number on the board, for example, 6. Ask the students “Can anyone figure out what 10 times this number is?” As a pre-assessment, spend some time exploring what the class knows about place value.
2. Each student should have paper and a writing utensil to record numbers.  Ask everyone to stand up.  Tell the students “We are going to record how many times we can jump (feel free to substitute your own movements: cartwheels, karate kicks etc) in 10 seconds. Write that number down on your index card.  Now let’s record how many push-ups you can do in 10 seconds.  Write that number down.”
3. Divide students into small groups.  Ask the students “What if we wanted to know how many you could do in 60 seconds? How could we solve that using our 6-second numbers?”  Each group should work together to make sure that as a group they have worked on each person’s answer. Add   As you monitor the groups, reinforce the idea of place value.
4. Now split the entire class in half.  Make 3 circles or boxes large enough to hold up to 9 students using cones, tape etc.  Each circle or box will represent one digit of a 3-digit number.  Take one of the student’s index cards that has a 3-digit number, for example 160.  Ask one person to represent the hundreds place by standing in the circle furthest to the left.  Ask the students “How many people do we need to represent the tens place?” Ask six people to stand in the box in the middle.  Ask the students “How many people do we need to represent the ones place?” Zero.  Have the students assess whether the number has been represented correctly by giving a thumbs up or thumbs down sign.  Pick another card with a different 3-digit number on it and repeat the same process. 
5. Say to the students “Now let’s start small.  Can you show me the number 3?” Three students will stand in the ones place.  Ask the students “What if we take 3 and multiply it by 10?”  Allow for students to respond with guesses of how the 3 ones should move.  The 3 students slide over into the tens place. Ask the students “What if we take 30 and multiply it by 10?”  Again, allow for students to provide the answer and discuss where the bodies should move.  The 3 students slide over again into the hundredths place.
6. Tell the students, “Now let’s add and subtract two numbers.”  Make another set of circles or boxes parallel to the first set.  Draw two more cards from students, for example, 120 and 150.  Ask students to represent each number in the boxes.  Ask the rest of the class to do the same procedure on paper as we watch it happen with bodies. Tell the class, “Let’s add 120 and 150.”  All the students representing tens should move into one box, all the students representing hundreds should move into another box so that the total equals 270.  The first time through you may need to count out the tens and hundreds together as a class.  As you repeat the process a few times, make sure each student does some of each kind of addition (with bodies/writing).  Continue to ask what’s happening with place value.  Notice what happens when a number is carried over, for example, 140 and 170. Spend some time reinforcing this concept of carrying numbers to make sure the students understand.  Provide guidance when needed.
7. Say to students “Now let’s take two of our numbers and compare them using <, =, >.  Ask students to represent two numbers in the boxes, for example 150 and 220.  Ask the other students to write these numbers down.  Ask the students “What symbol should go in between the two numbers?”  Ask one student to represent the symbol using two arms as an alligator mouth always wanting to eat the bigger number.  Ask the students who are writing to write the symbol with the alligator mouth facing the bigger number.  Ask the students “Which place value should we look at first? Why?”  Repeat this exercise a few times with different numbers.
8. To assess, write a whole multi-digit number on the board, for example, 800.  Ask a series of questions to which students can respond verbally.  ”How many tens are in this number?” (800 ¸  10  = 80) Allow time for discussion.  “Which number is bigger 130 or 410?  What is 3 times 10? What is 30 times 10? What is 300 times 10?”  As students respond to the questions, make sure to reinforce the core standards addressed in this lesson.