math journal submission 1
Traneka Wilson
Module3CheckYourUnderstandingPV.pptxECED 6263 Module 3 Check Your Understanding Problem Set
7 problems
Read the directions carefully
Be sure to use the methods asked for in the directions and to show steps so that your thinking can be understood
1. Model the number, 37, using the following:
Tens
Oness
An oral name written in standard form.
An oral name written in base-ten form.
A groupable model. Use one of the two formats shown to the right. You may use the objects on this slide or you may draw objects and submit .jpg, .png, or .pdf files.
d. A pregrouped model. Use one of the two formats shown to the right. You may use the objects on this slide or you may draw objects and submit .jpg, .png, or .pdf files.
Little ten frames Base ten blocks
Sticks and cups Snap cubes
2a. Explain why students should be introduced to groupable models and then pregrouped models to best develop place value understanding.
2b. Explain what nonproportional models are and why they are inappropriate to use to help students develop place value understanding.
This is a problem that was posed to students: Ardyn made 74 bracelets over summer break and then sold some. She now has 45 bracelets left. How many did she sell?
This is how one student solved the problem about Ardyn’s bracelets using a hundred chart:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 |
| 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| 51 | 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 |
| 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 |
| 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 |
| 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 | 90 |
| 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 |
The student explained her reasoning like this: “I can use the hundreds chart and start at 74. I can move up 3 spaces and 1 to the right to get to 45. She sold 31 bracelets.”
Is the student’s answer correct or incorrect?
If the student’s answer is incorrect, describe the mistake and what misunderstanding led to this mistake.
4. Show 259 four different ways with base ten blocks. The first way should be in the standard representation. List the amount of hundreds, tens, and ones in each way you show 259. You may use the objects on this slide or you may draw objects and submit .jpg, .png, or .pdf files.
Hundreds
Tens
Ones
First way
Fourth way
Third way
Second way
5. Answer the following questions below referring to these three numbers:
Which two numbers are closest? How do you know?
Which is closest to 500? To 650?
Name a number between 564 and 445.
Name a multiple of ten between 564 and 702.
Name an odd number that is less than all of these numbers.
564
702
445
About how far apart are 445 and 700? About how far apart are 445 and 7000?
If these are big numbers, what are some small numbers? What are some numbers that are about the same? What are some numbers that make these seem small?
6. Use the triples system to organize the following numbers by place value and write the numbers in words using place value language.
15,623,407,009 In words:
In the triples system:
| Hundred billion | Ten billion | One billion | Hundred million | Ten million | One million | Hundred thousand | Ten thousand | One thousand | Hundred units | Ten units | One unit |
| Billions | Millions | Thousands | Units | ||||||||
b. 508,934,059,600 In words:
In the triples system:
| Hundred billion | Ten billion | One billion | Hundred million | Ten million | One million | Hundred thousand | Ten thousand | One thousand | Hundred units | Ten units | One unit |
| Billions | Millions | Thousands | Units | ||||||||
7. Let’s explore some really large numbers in parts a and b below.
How many seconds have you lived? Explain how you found your answer.
Choose a wall in your home or somewhere at school. How many 3 by 5 index cards would it take to cover that wall? Explain how you found your answer.
