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Building Whole Numbers
Activity Summary: Using Base-10 blocks (or alternative paper cut-outs), the students get a feel for whole number place values. This activity guides students to see that place values grow by multiples of ten. Furthermore, students practice identifying place values and building numbers with their blocks.
Subject: Math - Numbers and Operations
Grade Level:
Target Grade: 5
Upper Bound: 6
Lower Bound: 4
Time Required: This activity should take about one 50-min class period. Activity Team/Group Size: Depends on quantity of materials and choice of activities. I would suggest groups no bigger than three.Materials List: Need either Base-10 blocks (available from any company which sells math-based manipulatives) or paper cut-out alternatives found in Connections book. (These can be made yourself. You need a 10x10 grid of unit squares, a 10x1 rod, and unit squares themselves. Note: If using paper alternatives, cube is tricky to construct.) For the recommended supplementary activities a plain six-sided die, playing cards, and a computer with internet capability are used.
Reusable Activity Cost Per Group [in dollars]: Cost of a Base-10 block classroom set for 25 kids is about $80, but these blocks translate into many different uses. If using paper cut-out alternatives, cost of copies. For the recommended supplementary activities a plain six-sided die and playing cards can be found at most stores for under $1.Authors:
Graduate Fellow Name: Amy Collins Undergraduate Fellow Name: Ryan Newman
Teacher Mentor Name: Laura Sebesta Date Submitted: 03/13/05Date Last Edited: 4/5/05
Activity Introduction / Motivation: Could begin by asking kids how you would make a millions block. However, I chose not to make this the focus of the activity.Activity Plan: *Big idea for 1-6: Place values grow by multiples of 10.*
1. Have students put their blocks in order, identifying a unit cube as 1, a rod as 10, a flat as 100, and a cube as 1,000.
2. Using the blocks, have them answer:
How many unit cubes in a rod?
How many rods in a flat?
How many flats in a cube?
How many unit cubes in a flat?
How many rods in a cube?
How many unit cubes in a big cube?
3. Write 1 10 100 1,000 on the board and get the kids to recognize that there is a relationship between adding a zero and increasing the value of the number; what is the relationship?
4. Still referring to numbers on the board, ask the students, What if I want to know how many 1s are in 100? Or how many 10s in 1,000? Goal is to get them to see that jumping two place values equivalent to jumping 10 x 10 = 100 in value.
5. Ask the kids how to make a ten-thousand block. (prompt: how many one thousand cubes would be in it?) How about a one hundred thousand block? Add these numbers to the ones already on the board. Can point out here that some numbers, when read aloud, (such as 10,000 and 100,000 give a clue to their value ten 1,000s or one hundred 1,000s.)
6. Ask kids what comes next. Most will probably know one million. What would a millions block look like? (prompt: Think about your ten and one hundred thousand blocks. How many would it take to build one million?) Add 1,000,000 to the numbers on board.
*Items 7-9 cover TEKS objective 1 (A) & (B) for 6th grade: Compare and order non-negative rational numbers and generate equivalent forms of rational numbers including whole numbers.*
7. Have the students build numbers with their blocks. E.g. 1,358 would be 1 one thousand cube, 3 hundred flats, 5 ten rods, and 8 unit cubes.
- First discuss addition by putting together the blocks for two numbers. Be careful to first give numbers which do not require carrying. Then go to numbers with carrying which leads into your next step. Dont use more than 2 digit numbers for adding at first.
- If students are building numbers starting with the ones (unit cubes) and working their way up, use a pyramid as an example to explain to students why you build numbers from the largest place value present down: When you build a pyramid, where do you start? With the top corner piece? No, you start at the bottom with the biggest piece/layer.
- Take one of the numbers you have had them build and modify it so they will recognize that ten of one block equals a new block for the place value one greater. E.g. With the number 1,358, add 2 unit cubes (students need to recognize the new number, 1,360 has another rod and no unit cubes) or add 5 rods (so the resulting number, 1,408, has no rods but another flat.)
8. To practice bigger numbers, students can list (either on the board or a sheet of paper) the building blocks needed. e.g. 1,005,769 = 1 one million, 5 one thousands, 7 one hundreds, 6 tens, and 9 ones. (Note: Write the numbers on the board and have a student read that number out loud).
- Once students seem comfortable with this, have them write out the numbers theyve built in expanded form. So the above example becomes (1 x 1,000,000) + (5 x 1,000) + (8 x 100) + (6 x 10) + 9.
- If students have been introduced to exponents, can then take these numbers and write in exponential (scientific) notation: (1 x 106) + (5 x 103) + (8 x 102) + (6 x 101) + (9 x 100).
9. With your list of numbers now written on the board, you can ask:
- Which number has a (pick a digit 0-9) in the (pick a place value) place?
- In this number, what digit is in the (pick a place value) place?
- Have them compare and order numbers.
10. After this introduction, the students can play some games dealing with place value. There are many of these available, but here are a few suggestions:
a. Have the students use the Base-10 blocks as currency. This activity will work best if the students are in small groups, but everyone should do some work in the group: rolling the die, counting blocks, checking, etc. Each group of students acting as one account should all start out with the same amount of blocks. One group starts with a die. They choose another group which will give them blocks as money based on what they roll. The first roll will determine the place value of the money to be given. 5 and 6 will count as 0 for this activity, but otherwise the place value will correspond to 10^(roll of the die) so if a 2 is rolled, hundreds will be given; a 5: 10^0=1, so ones will be given; etc. They will then roll again to determine how many of this value will be given. So, if a 1 is rolled the first time and a 5 the second, then the group chosen will give the group rolling the die 5 tens, making change as necessary. The students should quickly notice that rolling a 4 on the first roll of a turn should wipe the other group out unless they have enough to cover 10,000. Then, the group which paid gets to choose a group and rolls the die, takes the amount determined from the group they chose, and so on until one group has all the blocks, or until time is up, when the blocks are counted and the totals are compared.
b. Many games can be found on the internet dealing with place value. One which is appropriate and fun can be found at ( HYPERLINK "http://education.jlab.org/placevalue/" http://education.jlab.org/placevalue/). In this activity, random numbers are generated in a specified range and the students must decide which place value to put the numbers in as they come, without knowing the next numbers. The goal is to try and make the largest number they can in the end, so they should discover quickly that the large numbers should be put in the larger place values. Before the activity begins the game asks for the number range to draw from, the number of places in the number, and the number of extra discard places for numbers which will not be used. These should be chosen at appropriately simple levels at the beginning (5 digits, largest digit 6, and 3 discards for instance) and then adjusted as the students become more familiar with the game. An extra suggestion is to try and have the students use the Base-10 blocks to model the number as the digits are selected. It proves to be quite difficult to create the largest number possible given that the numbers are random, but the importance of the activity lies in understanding that larger digits in larger place values will yield greater total values. If they find the activity too frustrating, a modified version is given in part c.
c. Human version of the place value game from b.: Put playing cards, 4 each of 1 7, in an envelope. The dealer pulls out 8 cards, one at a time, reading them to the other 2 players. The other 2 players write the numbers on a paper in 6 digit blanks and 2 discard blanks attempting to create the largest 6 digit number they can. After the 8 numbers are pulled and written, the player with the larger number wins. If the students can add numbers of this size, then repeat the game 3 times with a different player as dealer each time, and the winner is the player with the largest total of the two games for which they were not the dealer.
d. There are a few other suggested links in the references section, along with other resources for understanding place value.
Assessment: This lesson plan is based a great deal on prompting students for answers, so if the class seems involved in answering the questions, they are probably catching on. Grouping the students into small groups will help you see if they understand the ideas during the number-building phase. There are TAKS review questions addressing the material covered in items 7-9. Having students answer such questions would provide an indication of how well they followed the lesson. The place value games will also provide as a good guide for how well they understand the material.
Learning Objectives:
Place values grow by multiples of ten
Identify place values
Represent numbers in standard, expanded, and exponential form
Compare and order (large) whole numbers
Prerequisites for this Activity: A previous introduction to place value would be helpful; this activity is probably more to reinforce concepts than to teach them.
Troubleshooting Tips: Students may get confused when asked how many 10s are in 1,000 and answer three since 103 = 1,000. This is a good time to point out the subtle difference between adding three 10s and multiplying three 10s. Similarly they should understand the difference between adding one hundred 10s and multiplying one hundred 10s. The question How many 10s in 1,000? is asking for the former. The question How does moving three place values to the left change the value of the number? is the latter.
References:
- Make a Million, Brummett, Micaelia R., and Linda H. Charles. Connections: Linking Manipulatives to Mathematics (gr 6). Chicago, IL: Creative Publications, 1989. 4-7.
- HYPERLINK "http://education.jlab.org/placevalue/" http://education.jlab.org/placevalue/ - activity b. from 10. in the activity plan above
- HYPERLINK "http://www.funbrain.com/tens/" http://www.funbrain.com/tens/ - a simple place value activity
- HYPERLINK "http://www.arcytech.org/java/b10blocks/b10blocks.html " http://www.arcytech.org/java/b10blocks/b10blocks.html - instruction page may be a useful reference for base-10 blocks
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