Exploring Place Value – Race the Clock for Third Grade!

This resource was created by Big Ideas in Beta, a Big Ideas Fest project, with acknowledgement to Amanda Dolan

1. Tell students, “Today we are going to explore the properties of place value.” As a pre-assessment, spend some time brainstorming what the students know about place value and why it is important.  Write the students’ ideas up on a piece of chart paper that can be posted in the classroom at the end of the lesson.    Take the students outside or to an open area like a gymnasium. Tell the students, “Today, we are going to do a number of activities for one minute each.  We are going to race the clock and see how many times you can complete each activity within that minute.”  Each student should have a piece of paper and a writing utensil to record their numbers.
   
2. Begin the activities.  You should start with a set of activities that you have selected.  Possibilities are jumping jacks, sit ups, push ups, hopping on one leg, but there are so many more.  Be creative!  Later on, you can ask the students to contribute ideas for additional activities to time. Remind students that they also timed these activities in second grade and challenge them to go more quickly and complete more of each activity per minute, now that they are older. 
3. Once the students have completed all the activities and recorded their numbers for each activity, put them into small groups.  The group sizes can vary according to what seems manageable for your class of students. It is best to have an even number of groups as this is helpful for the comparison activity later in the lesson. Ask each group to combine/add their numbers for each activity so that they have one group number for each task.
   
4. Once they have their group numbers tell the class, “I wonder how many sit-ups/pushups/etc. your group would be able to do if it had forty members instead of four (or whatever ten times the number of students in the group is).  How could we figure that out?” Give the groups time to problem solve, working together to reach an answer.  As they work, walk around and monitor, being sure to introduce the idea of place value into the solution process when appropriate. 
   
5. Once they have had time to reach a solution, give the groups time to share their answers and explain their processes for solving the problem.  Make sure to highlight the use of place value when multiplying by ten.  For groups that finish before others, challenge the students to multiply by twenty, thirty or other multiples of ten. Explain to the students that they can use any of the tools available to them – unifix cubes, paper, their bodies - to represent their largest number/multiples of ten. Demonstrate with one group how they can use four people to represent a four digit number by using a shape or an action to convey each of the ones, tens, hundreds and thousands places.  For example, to represent the number 5214, the first person might jump five times, the second person twice, the third person once, and the fourth person three times. (Groups should feel free to creatively choose whichever actions they like to represent the ones, tens, hundreds and thousands places). Alternatively, the first person can make the shape of the number 5, the second person the shape of the number 2, the third person the shape of the number 1 and the fourth person the shape of the number 4. Walk around and monitor the groups’ progress, stopping to help or facilitate where necessary. Challenge each group to come up with three to four different ways to represent the group numbers they have recorded so that they demonstrate the rules of place value.  Again, encourage them to use any of the available tools. Spend some time allowing the groups to share their representations. Groups should discuss which representations of the group numbers were easiest to understand and why.  As you manage the discussion, make sure that students understand the importance of place value and how it can be used as a mathematical tool and that you highlight the core standards addressed in this lesson.
6. Direct the groups to write on large cards the largest numbers/multiples of ten they had for each activity. There should be only one number on each card so that, for example, the group number of jumping jacks is represented on one card and the group number of sit-ups on another. Starting with cards from two different groups for the same activity (for example one group may have done 234 jumping jacks and the other 198), place the cards at opposite sides of the open space.  Review with students the rules of comparisons.  Practice making comparison symbols with their bodies, using their arms to make the greater than/less than symbol.  Remind them of the analogy of the alligator mouth eating the larger number.  Ask students, “Which place, ones, tens, hundreds or thousands, should we consider first when comparing two numbers?”  Allow time for discussion.  Tell the entire class to stand between the two number cards on the ground.
   
7. Direct students to create their comparison symbol with their arms and begin walking towards the larger number as their giant mouth (arms) eats it. Now, split the original groups from the first activity into pairs so that sets of two groups are comparing their totals for each of the various activities.  As they compare, they should set their cards on opposite sides of the space and the entire group should move towards the larger number with their arms munching away. For an extension, put down a card from each group for the same activity (for example, every group’s total for jumping jacks). 
   
8. Challenge students to compare all the groups’ totals with a student standing between each number card making the comparison symbol.  The number cards should finally arrange from smallest to largest with the comparison symbols all facing the correct direction. Go back to class and reexamine the notes you made on the chart paper at the beginning of the lesson.  As a post-assessment, discuss with students what they learned.  Ask them, “Did any of your previous ideas about place value change?  How does place value help us when adding large numbers?  How does it help us when comparing two or more numbers?”  Add any new insights to what is already written on the board, making sure to reinforce the core standards addressed in this lesson