Mission 1 Summary
Mission 1 Summary
Embedded Files
Learning Objectives
Students will be able to:
Develop proficiency in recognizing patterns of multiplication by ten within the base ten system.
Utilize place value charts to comprehend the magnitude of large numbers and their respective places.
Apply place value concepts to compare whole numbers effectively.
Learn rounding techniques for any place value, transitioning from visual aids to mental calculations.
Solve word problems using algorithmic strategies based on place value understanding.
Introduce the use of variables to represent unknown quantities in problem-solving contexts.
A place value chart shows the value of each digit in a number based on where it is placed. Here's a simple way to understand it:
Ones: The rightmost column, where each digit represents a single unit.
Tens: The next column to the left, where each digit represents ten units.
Hundreds: The next column to the left of tens, where each digit represents a hundred units and it continues like this for larger numbers for thousands, ten thousands, etc
Example:
Let's break down the number 4,752 using a place value chart.
4 is in the thousands place, so it represents 4,000.
7 is in the hundreds place, so it represents 700.
5 is in the tens place, so it represents 50.
2 is in the ones place, so it represents 2.
So, the number 4,752 is made up of 4,000 + 700 + 50 + 2.
⇒ Each unit in 1 place value is 10 times as large as a unit in the place value to its right.
1 ten = 10 × 1 one (1 ten is 10 times as much as 1 one.)
1 hundred = 10 × 1 ten (1 hundred is 10 times as much as 1 ten.)
1 thousand = 10 × 1 hundred (1 thousand is 10 times as much as 1 hundred.)
Also,
10 × 1 thousand = 10 thousands = 1 ten thousand
10 × 1 ten thousand = 10 ten thousands = 1 hundred thousand
10 × 1 hundred thousand = 10 hundred thousands = 1 million
⇒ Multiply multiple copies of two units by 10 with the help of a place value chart.
Step 1: Write the numbers in the place value chart according to their place value.
Step 2: When you multiply a number by 10, you shift the digits one place to the left to the larger unit and put a zero in the ones place.
⇒ Divide multiple copies of two units by 10 with the help of a place value chart..
Step 1: Write the numbers in the place value chart according to their place value.
Step 2: When you divide a number by 10, you shift the digits one place to the right to the smaller unit.
Thousands: Commas are placed after every group of three digits, starting from the right.
Examples:
Examples:
Let's break down a few numbers to illustrate:
1,234: The comma separates thousands from hundreds. Here, it helps to distinguish between 1 thousand and 234.
12,345: In this number, the comma separates thousands from hundreds and tens. It helps to see that it's 12 thousand, 345.
123,456: This comma separates hundreds of thousands from tens of thousands and thousands. It helps to recognize it as 123 thousand, 456.
Standard form: The standard form of a number is representing larger numbers in a way that is easy to read and write.
Example: 234 is written in its standard form.
Unit form: The unit form of a number is a way of expressing a number as the sum of its individual units, with each digit representing a specific place value.
Example: Unit form of 3,724 is 3 thousands 7 hundreds 2 tens and 4 ones.
Word form: Word form represents a number using words. It is a way of expressing a numerical value in written or spoken form.
Example: Word from for 3,724 is 3 thousand 7 hundred twenty- four.
Expanded form: Expanded form is a way of representing a number as the sum of its individual place values. In other words, it breaks down a number into the sum of its digits multiplied by their respective place values.
Example: In expanded form, this number is expressed as:
4,583= 4,000+500+80+3.
Or
4,583 = (4 x 1000 )+ (5 x 100) + (8 x 10) + (3 x 1)
Example: Representing 708430325 in the following ways:
Comparing multi digit whole numbers:
When comparing multi-digit whole numbers, you are essentially determining which number is larger or smaller.
Example:
Compare 7,352 and 7,248.
Start from the leftmost digit:
In the thousands place, both numbers have a 7. Move to the hundreds place: 3 vs. 2. Since 3 is greater than 2, 7,352 is greater than 7,248.
So, in this case, 7,352 is greater than 7,248.
[We can place the numbers in the place value chart for the better understanding]
Rounding four digit numbers to the nearest thousand using vertical number line:
Rounding off numbers to the nearest thousand using a vertical number line involves visualizing the number line and placing the given number on it. Here's a step-by-step guide:
Example: Let's take the number 3,890 as an example and round it to the nearest thousand
Step 1: Draw a Vertical Number line
Step 2: Locate the position of 3,890 on the number line. It falls between 3000 and 4000.
Step 3:Mark the upper end as 4,000 and lower end as 3,000 on the number line
Step 4: Mark the midway point as 3,500
Step 5: 3,890 is more than midway point,
Step 6: Therefore, 3,890 rounded to the nearest thousand is 4,000
Rounding four digit numbers to the nearest ten thousand without using a vertical number line:
Rounding off numbers without using a vertical number line involves identifying the place value to which you want to round. Here's a step-by-step guide:
Step 1 : Between what two ten thousand is 548,253?
Answer : 540,000 and 550,000.
Step 2 : What is halfway between 540,000 and 550,000?
Answer : 545,000
Step 3: Is 548,253 less than or more than halfway?
Answer : More than.
Step 4 : 548,253 is nearer to 550,000.
Step 5: 548,253 rounded to the nearest ten thousand is 550,000.
Addition of multi-digit whole numbers:
Adding multi-digit whole numbers involves combining numbers with multiple digits by adding each place value from right to left.
Tape diagram:
A tape diagram, also known as a strip diagram, bar model, or fraction strip, is a visual representation to help students visualize and solve problems. Students can use them to model and solve various types of mathematical problems, such as addition, subtraction, multiplication, division, and fraction problems. Let’s learn more with an example:
Example:
Norfolk has a population of 242,628 people. Baltimore has 376,865 more people than Norfolk. What is the total population of Baltimore?
Step 1: Draw tape diagram according to the information given in the question
Step 2 : Solve the problem using standard algorithm
⇒ Start by adding the digits in the rightmost column (ones place): 8 + 5 = 13.
Write down the 3 and carry over the other 1 to the next column.
⇒ Move to the next column (tens place) and add the carried-over 1 along with the digits in this column: 1 (carried over) + 2 + 6 = 9. Write down the 9 in the result
⇒ Move to the next column (hundreds place)add 6 + 8 = 14. Write down the 4 and carry over the other 1 to the next column.
⇒ Continue the same with the other place value. Mark your final answer as 619,493
Step 3 : Complete the problem with a final statement.
The total population of Baltimore is 619,493.
Subtraction of multi digit whole numbers:
Subtracting multi-digit whole numbers involves subtracting each place value from the corresponding place value in the other number, starting from the rightmost digit.
Let’s see an example:
Bryce needed to purchase a large order of computer supplies for his company. He was allowed to spend $859,239 on computers. However, he ended up only spending $272,650. How much money was left?
Step 1: Represent the problem with a tape diagram. In your tape diagram record the whole as 859,239 known part as 272,650 and mark the unknown part with a letter
Step 2 : Solve the problem using standard algorithm
⇒Start with the rightmost digit (ones place). 9 - 0 = 9
⇒ Move to the next place value (tens place). Subtract 5 from 3. Since there are not enough tens, we need to borrow from the next higher place value (hundreds place). Borrow 1 ten from the hundreds place, making it 1. Now subtract 5 from 13( 13 - 5 = 8 )
⇒ Subtract the next place value ( hundreds). There is not enough hundred to subtract 6, we need to borrow from the next higher place value ( thousands place). Borrow 1 hundred from thousand, making it 8. Now subtract 6 from 11 ( 11 - 6 = 5 )
⇒ Continue the same with the other place value. Mark your final answer as 586,589
Step 3: Complete the problem with a final statement.
Bryce was left with $586,589.
Addend: E.g., in 4 + 5, the numbers 4 and 5 are the addends
Algorithm: A step-by-step procedure to solve a particular type of problem.
Bundling, making, renaming, changing, exchanging, regrouping, trading:
E.g., exchanging 10 ones for 1 ten
Compose: E.g., to make 1 larger unit from 10 smaller units
Decompose: E.g., to break 1 larger unit into 10 smaller units
Difference: Answer to a subtraction problem
Digit: Any of the numbers 0 to 9; e.g., What is the value of the digit in the tens place?
Expression: A number, or any combination of sums, differences, products, or divisions of numbers that evaluates to a number
Example: 3 + 4, 8 × 3, 15 ÷ 3 as distinct from an equation or number sentence.
Equation: A statement that two expressions are equal
Example: 3 ×4 = 12 , 5 × b = 20 , 3 + 2 = 5
Number sentence (also addition, subtraction, multiplication, or division sentence):
An equation or inequality for which both expressions are numerical and can be evaluated to a single number
Example: 4 + 3 = 6 + 1, 2 = 2, 21 > 7 × 2, 5 ÷ 5 = 1
Number sentences are either true or false:
Example 4 + 4 < 6 × 2 and 21 ÷ 7 = 4) and contain no unknowns.
Variables: Letters that stand for numbers and can be added, subtracted, multiplied, and divided as numbers are
Symbols:
= : Equal to
< : Less than
> : Greater than
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