Exploring Place Value – Race the Clock!

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

LEARNING OUTCOMES:

• Students will explain place value through the hundreds place. 

• Students will investigate the relationships between numbers and how place value can be used to add and subtract larger numbers.

• Students will practice reading and writing numbers to 1000. 

• Students will work together to creatively problem solve

COMMON CORE STANDARDS ADDRESSED:  Understand Place Value.

• 2.NBT.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: 100 can be thought of as a bundle of ten tens — called a “hundred.” The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
• 2.NBT.2. Count within 1000; skip-count by 5s, 10s, and 100s.
• 2.NBT.3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 
• 2.NBT.4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons 
• 2.NBT.5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 
• 2.NBT.6. Add up to four two-digit numbers using strategies based on place value and properties of operations.
• 2.NBT.7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
• 2.NBT.8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900. 
• 2.NBT.9. Explain why addition and subtraction strategies work, using place value and the properties of operations.

TIME REQUIRED FOR LESSON:

45 minutes to one hour

TIME REQUIRED FOR TEACHER PREPARATION:

Less than ten minutes

MATERIALS FOR LESSON:

• A stopwatch or watch with a second hand
• Set of unifix cubes for each group of students
  
• Paper, pencil and crayons or markers 
• Large blank cards for recording group totals

OVERVIEW OF LESSON:

1. Tell the students, “Today they 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. 
2. 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.
3. 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. 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.
4. Ask each group to combine/add their numbers for each activity so that they have one group number for each task.  Explain to them that they can use any of the tools available to them – unifix cubes, paper, their bodies - to represent their numbers. Demonstrate with one group how they can use three people to represent a three digit number by using a shape or an action to convey each of the ones, tens and hundreds places.  For example, to represent the number 214, the first person might jump twice, the second person jump once, and the third person jump three times. (Groups should feel free to creatively choose whichever actions they like to represent the ones, tens and hundreds places). Alternatively, the first person can make the shape of the number 2, the second person the shape of the number 1, and the third person the shape of the number 4. Walk around and monitor the groups’ progress, stopping to help or facilitate where necessary.
5. 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.
6. Spend some time allowing the groups to share their representations. Groups should explain strategies they used for adding up their individual numbers to combine for a group number.  They should also 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.
7. Direct the groups to write on large cards the group totals 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. 
8. Tell the students, “Now we are going to look at some comparisons.” 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 or hundreds, should we consider first when comparing two numbers?” Allow time for discussion. 
9. As an introduction to the comparison activity, tell the entire class to stand between the two number cards on the ground.  Direct students to create their comparison symbol with their alligator 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 two numbers, 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.
10. For an extension, put down a card from each group for the same activity (for example, every group’s total for jumping jacks).  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.
11. Go back to class and reexamine the notes you made on the board at the beginning of the lesson. As a post-assessment, ask the students “Did any of what you thought you knew about place value change?” Allow time for discussion.  Add any new insights to what is already written on the chart paper, making sure to reinforce the core standards addressed in this lesson.