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Compare Multi-Digit Whole Numbers

If students really understand place value, then they can get a stronger grasp on other mathematical operations!  I like to start by asking students how many digits are in the universe?  And most times students say infinity!  Because fourth graders love the idea of infinity.  But in fact, there are only ten digits!  It’s mind boggling.  Infinity is only accomplished because of place value, not just the digits and numbers.  And the key is understanding the value of each place. So we introduce Comparing Multi-Digit Whole Numbers.

Students have used place value charts and place value blocks for comparing whole numbers, but what really helps them understand the value of place value is when I introduce it as weights.  Weights are a value that we can really feel.

My students have used place value charts and even made some of their own, But we can really start to apply knowledge of place value when we introduce comparing multi digit numbers using weights.

Set up for the Activity for Comparing Multi-Digit Whole Numbers

1. Print out the weight plate sheets (pages 5-10 of the worksheet) for students to cut out.
2. Provide each team one set of weight plate sheets (pages 5-10 of worksheet).  This will give the teams 10 plates of each weight.
3. Cut out strips of paper or place masking tape on the desks.  This will represent the weight bars.
4. Have a large book or cardboard divider to place in the center of the weight bar.
5. Provide each student the Comparing Multi-digit Whole Numbers Activity Worksheet.
6. Bring in weights or dumbells, or have images of weight lifters/ weight bars to introduce the activity.  (If you do not have any weights, you could bring in objects like a single size serving of milk and a gallon of milk to represent 1 pound and 10 pound weights – or – 1 thin book and a stack of 10 books, or large dictionary).
7. Gather base ten blocks to use to help students visualize place value.
8. Review the inequality symbols: =, <, >
9. Draw or provide a place value chart on the board with an example of weights, the numbers, the comparison.  Students must circle the weight plate and underline the place in the number that determines which number is greater.

Launch the Activity for Comparing Multi Digit Whole Numbers

Bring in weights or dumbbells if you can.  Otherwise have some of the following: a single book, and a stack of ten books; a cup of water and a gallon of water; a 1 lb weight and a 10 lb weight.  (Items do not have to actually weigh one and ten pounds, but the idea is to show how much heavier the weight gets when it becomes 10 times bigger, just like place value).

Tell the students that today they will be doing some weightlifting.  They have to use their imaginations, because they will be lifting some extraordinary weights.

Hold up the 1 lb dumbell and tell them that it is 1 pound.  You can have a volunteer come up and hold it.

Then hold up the 10 lb dumbbell.  Show how it looks bigger and have a volunteer or two try to hold it.  (Be sure to tell students to be careful with the heavier weights so no one gets hurt.)

Then compare the two weights by using base ten blocks.  You can hold up a single block and a long and ask which block represents which dumbell and why?

Then say something like, “Well, if this is 1 pound, and the next weight is 10 pounds, I would need 10 of these to equal this.”  You can line up the base ten blocks to show this.

Then say “I don’t have a larger dumbbell, but if my weights represented place value, how heavy will the next weight need to be?”

Ten 10-lb weights which equals 100 pounds!  And marvel at how hard it would be to lift that with one hand!  (Or at all).

Then explain that weightlifters can lift heavier loads when they use both hands.

Show a quick section of this video of a weightlifter (or use a visual) to help introduce the weight bar and weights.

Ask if anyone has a weight bench at home or has seen a weight bench.

Explain that today they will be working in teams.  As a team, 1 player must choose and hang some weights on his/her end of the bar while the partner records the number in standard form.  Tell your students to work quietly, because while one team is hanging their weights, the other team is working on the other side of the weight bar.  This team is also hanging weights and recording the number.

When time is up, the teams remove the divider and look at the weight bar.  Which side is heavier?

Together, they must determine and show which weight plate or place value made the side heavier or lighter.  They must record both team numbers and write <, > or =.  Then they must circle and name the place value that made the side heavier.  If the teams happen to hang the same weights they both earn 10 points.

The game continues with various rounds such as:  Closest to a 100, A number with 3 in the thousands place, a 5 digit number, a 3 digit number, a number with 3 zeros, etc…

Before splitting up into teams, demonstrate and “think aloud” to show an example.  Here is an example for a 4 digit number:

• Invite students to help model by saying, “We will model a 4 digit number – is there a volunteer who would like to hang some weights?”
• A student can come up and place weight plates on the board, or hold up a selection at his or her desk.
• Then you can select weight plates yourself and show them on the other side of the weight bar.
• For example: you take 2 thousands, 1 hundred, 3 tens and 5 ones.
• Maybe the student holds up 2 thousands, 2 hundreds, 2 tens and 3 ones
• The weight bar would look like this: (Note – usually weight bars have the smaller weights on the end of the bar (like the side on the right), however, for place value, it is easier to read it this way, so encourage both sides to place weight plates with the larger values on the left, just like place value.)

• Ask the class which is “heavier”?
• Then ask the class to write both of the numbers in standard form.
• Compare the numbers and the visual together.
• Ask questions, such as: “Which is heavier in the thousands place?  (neither – they are the same).  Or “Which has more hundreds?”

Weightlifting: Comparing Multi Digit Whole Numbers Activity

Teams of students will work to hang weight plates and write multi digit numbers.

1. Student teams cut out (and color) the weight plates.  They should have 10 of each size.  See pages 5-10 on the worksheet.
2. Place tape or a thin strip of paper across the desk and have a cardboard divider or book to prevent teams from seeing the other end.
3. Teams read the category, discuss what the category description means, and hang their weights so their number fits the category description.
4. Students need to have the weights and record the number in standard form.
5. When both teams are ready, remove the divider and compare the weights.
6. First compare the visual weights and see which is heavier; then compare the standard form to determine which is heavier.
7. Record BOTH numbers on the worksheet.
8. Circle the place value that determined which side was heavier.  The team that has the heavier number earns 1 point.
9. If the numbers are EQUAL, then both teams earn 10 points.
10. Continue play, making sure to follow the category name, record numbers and compare.

Reflecting on the Comparing Multi-Digit Numbers

When the teams have completed the activity, they can do some “free play” comparisons as well.

Have teams share some of their favorite rounds or weightlifting feats.  (Some groups may have very unbalanced bars, others may have unbelievably large sets of weights on each side).

Talk about the unrealistic parts of the activity.  And have students work together to create a possible realistic weight bar with their paper weight plates.  Think about how much weight a person might really be able to lift, and see if the students keep it balanced or re-order the weights.

Give the students a scenario: “What if you placed 13 blue rectangles (ten pounds).  What would that be equal to?”

Have students complete the worksheet p. 4 with more reflection questions that can be discussed and/or written in small groups or with the whole class.

Extensions on Comparing Multi-Digit Numbers

1. Students can draw a weightlifter, including his facial expression, and show a basic place value chart that clearly shows each place value.For example:A weightlifter with 1 pound, then 10 pounds, then 100 pounds, then 1 thousand pounds etc…Each time a plate is added, it is like adding a place or zeros.
2. Play a multi digit card game:Using a standard deck of cards, take out the face cardsStudents play rounds of 3,4,5,6,7,8 digit numbers.Round 1- 3 digit numbers: Each player places a 3 digit number, compares.  Whoever wins, wins the cards.Round 2 – (4 digit): The place 4 cards (4 digit number), compare.Round 3 – (5 digit): etc…Play continues until you run out of cards.

FREE Comparing Multi-Digit Whole Numbers Worksheets and Resources

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Comparing Multi Digit Numbers Worksheets and Resources

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