In this lesson, students will use Kidspiration Base Ten Blocks™ to model multiple representations of two-digit numbers on a place value mat. As students make connections between equivalent representations, such as modeling 13 with 1 ten and 3 ones or with 13 ones, they will not only learn important place value concepts and develop their number sense, but also build a solid conceptual foundation for later work with regrouping in the base-ten number system. Students will express their answers both visually with a model and numerically in a place value table.
Open the lesson by telling students that you would like to buy a piece of candy for 17¢. You have a jar of coins and would like help coming up with all of the different ways that you might pay for your candy without needing change back. Encourage students to come up with all possible combinations of pennies, nickels and dimes.
Explain to students that they can represent numbers in multiple ways just as they can represent money in multiple ways. Go to Kidspiration Starter>Activities>Math and open the Exploring Place Value.kia activity.
The first page of the activity is an example. It may be beneficial to walk through the example from the beginning as a class. If so, the first page of the activity can be unlocked ahead of time from the Teacher menu, allowing deletion of base ten blocks and numbers inside the table. Encourage students to think of different ways to represent the number 13. If students are stuck, ask them the following:
Can you represent 13 using a flat? If so, how many? If not, why not?
Can you represent 13 using a rod? If so, how many? If not, why not?
Can you represent 13 using only units? If so, how many? If not, why not?
Demonstrate how to bring blocks onto the place value mat. In addition to showing students how they can drag blocks, also show how they can point to anywhere on the workspace and then click successively on the desired block in the Math palette. This will help students bring out large quantities of blocks. Also demonstrate how to distinguish each representation with color and complete the table in the upper-right corner of the workspace to match their representations.
Note: For this activity, there is room in the table for students to record up to three numerical representations. Remind students that there may be more than three or less than three different representations, and that they should find as many as they can, up to three.
Allow students to work individually or in pairs to complete all four pages of the activity. Some students may figure out shortcuts, such as bringing 3 tens onto the workspace and using the Break Apart button on the Bottom toolbar to break them into 30 units, rather than bringing out 30 individual units. Encourage these strategies because they indicate important learning about trading, or regrouping, which will prepare them for later work with efficient procedures for operating on numbers, such as borrowing and carrying.
Conclude by showing a completed activity (for a sample, go to Kidspiration 3 Teacher menu>Teacher Resources Online>Lesson Plans>Grades K-2 Math>Exploring Place Value and open Place_Value_Exemplar.kid or have individual students present their solutions). Discuss the following as a class:
How are the representations on each page the same? How are they different?
Which representations used the least blocks? If you want to use as few blocks as possible to represent a number, is it better to use as many units as you can or as many rods as you can?
Will some numbers have more than three different representations? What is an example?
Did you discover any shortcuts while working on the activity?
What patterns do you notice in the tables?
Assess students on their completed activities, checking for the correct number of blocks and correct placement of blocks on the place value mat. Confirm that the information in the table corresponds with each representation.
Add pages to lengthen the activity or add an increasing variety of numbers. Consider including numbers in the hundreds or thousands.
Connect this activity to equivalent representations elsewhere in the world. In Picture View, students can use coins from the Money Symbol library under Math and Numbers to show multiple representations of dollar amounts. For an example, see Making Change.kia located here: Kidspiration Starter>Activities> Math.