1
Q
Define:
decimal numbers
A
Represent parts of a whole number, including a whole number and a part.
Examples: 0.74, 4.7 and 100.001
2
Q
Explain:
What is the place value to the left of the decimal point?
A
The place values to the left of the decimal point are represented as powers of ten:
- ones
- tens
- hundreds
These increase as you move left from the decimal point.
3
Q
Identify:
The place values starting at the decimal point.
A
- Tenths
- Hundredths
- Thousandths
- Ten-thousandths
4
Q
Name these decimal numbers:
- 2.3
- 15.78
- 0.009
- 30.0475
A
- 2.3 → Two and three tenths
- 15.78 → Fifteen and seventy-eight hundredths
- 0.009 → Nine thousandths
- 30.0475 → Thirty and four hundred seventy-five ten-thousandths
5
Q
Explain:
How do you compare decimal numbers?
A
- Write the decimals with the decimal points lined up.
- Compare from the leftmost place value to the right.
Use the larger digit to determine which decimal is greater.
6
Q
Explain:
The first step in ordering decimals.
A
Write the numbers with the decimal points lined up.
This ensures that place values correspond correctly.
7
Q
Explain:
How do you determine which decimal is bigger?
A
- Write the decimals with decimal points lined up.
- Compare each place value starting from the left until you find a difference.
The number with the larger digit at the first point of difference is greater.
8
Q
Explain:
The process for ordering decimal numbers from least to greatest.
A
- Write the numbers with decimal points lined up.
- Compare from the leftmost place value to the right.
- Identify and disregard numbers already determined as larger.
Continue until all numbers are ordered.
9
Q
Explain:
What is the process for ordering decimals from greatest to least?
A
- Write the numbers with decimal points lined up.
- Compare from the leftmost place value to the right.
The process is similar to ordering from least to greatest.
Identify and disregard numbers already determined as smaller.
10
Q
Explain:
The significance of adding zeroes when comparing decimals.
A
It helps align the place values with different numbers of digits.
This does not change the value of the numbers.
11
Q
Define:
Base ten blocks
A
Concrete manipulatives that replicate the base ten model of counting.
They help visualize the size of numbers by representing each place value.
12
Q
Describe:
The base ten model of counting.
A
A system where amounts are represented by digits 0 through 9.
After 9, numbers increase in place value with each new digit.
13
Q
Identify:
The different types of base ten blocks.
A
- Unit blocks (ones)
- Rods (tens)
- Flats (hundreds)
- Cubes (thousands)
Each type represents a specific place value.
14
Q
Identify:
What does a unit block represent?
A
One.
It is a single cube, about 1 cubic centimeter in volume.
15
Q
Identify:
What is a rod made of base ten blocks?
A
10 unit blocks stacked together.
It represents 1 ten and is usually 10 centimeters long.
16
Q
Identify:
What does a flat represents in base ten blocks?
A
100 unit blocks or 10 rods.
It is 100 times the size of a unit block.
17
Q
Identify:
The value represented by a cube in base ten blocks.
A
1,000 unit blocks, 100 rods, or 10 flats.
It represents the digit in the thousands place.
18
Q
Explain:
How do base ten blocks demonstrate place values?
A
- Unit blocks for ones
- Rods for tens
- Flats for hundreds
- Cubes for thousands
No blocks are used for digits with a value of zero.
19
Q
Explain:
How would you represent 3,427 using base ten blocks?
A
3 cubes, 4 flats, 2 rods, and 7 unit blocks.
This shows the values of thousands, hundreds, tens, and ones, respectively.
20
Q
Explain:
How would you represent the number 105 with base ten blocks?
A
1 flat, 0 rods and 5 unit blocks.
The flat represents the hundreds place, while zeros indicate no blocks.
21
Q
Identify:
The largest base ten block.
A
The cube.
It represents the digit in the thousands place.
22
Q
Identify:
The purpose of using base ten blocks.
A
To represent numbers and understand place value.
They also help model operations like addition, subtraction, multiplication, and division.
23
Q
Define:
A number line
A
A straight line labeled by equally spaced integers, extended indefinitely from either side of zero.
It includes both negative and positive numbers, known as integers.
24
Q
Identify:
6 steps to draw a number line.
A
- Label a point with zero.
- Draw a straight line to the right with an arrow.
- Draw a straight line to the left with an arrow.
- Mark points equally separated on either side of zero.
- Points to the right are positive integers.
- Points to the left are negative integers.
The ends of the number line have arrows to indicate infinite numbers.
25
# Identify:
The **types** of **numbers** that can be represented on a **number line**.
**Rational numbers**, which include:
* Integers
* Fractions
* Finite or repeating decimals
## Footnote
Pi is an example of a non-rational number as it does not stop or repeat.
26
# Explain:
How can **rational numbers** be **graphed** on a **number line**?
1. **Regular number line**: Use a point to label the rational number.
2. **Zooming in**: Use smaller lines to represent fractions or decimals.
## Footnote
Example: For -1/3, grids can be used to separate the rational numbers by 1/3.
27
# Explain:
How do you **represent** **3/4** on a **number line**?
Divide the space between 0 and 1 into increments of 1/4 and mark the 3/4 position with a dot.
## Footnote
Make sure the integers are separated enough to clearly distinguish the fractions.
28
# Define:
rational number
Any **positive** or **negative** **number** that can be expressed as a fraction.
29
# Define:
fraction
Mathematical **representation** of **dividing** two **integers**.
## Footnote
Most commonly used when conducting rational number calculations.
30
# Define:
denominator
The **bottom** integer in a **fraction**.
## Footnote
For example, in the fraction 1/4, 4 is the denominator.
31
# Define:
numerator
The integer on the **top** of a **fraction**.
32
# Define:
least common denominator
| (**LCD**)
The **smallest number** that all denominators can go into.
## Footnote
It should be **used to find a common denominator**.
33
# Describe:
What is **required** to **add** or **subtract** rational numbers in **fraction form**?
Identify a **common** **denominator**.
| A common denominator is a multiple of both denominators.
## Footnote
The denominators must be identical for the operation.
34
# Identify:
The **first step** in **adding** **rational numbers**.
Find the least common denominator (**LCD**).
## Footnote
This ensures the fractions can be added together.
35
# Explain:
How do you **find** the **LCD** of **two fractions**?
1. **Find** the prime factors of each denominator.
2. **List** the prime factors including the greatest number of times each appears.
3. **Multiply** the list of factors together.
## Footnote
Example: The LCD of 24 and 16 is 48.
36
# Explain:
The **process** to **add fractions** once the LCD is found.
Convert each fraction to an equivalent fraction using the **LCD**, then **add** the **numerators**.
## Footnote
Retain the LCD as the denominator of the final answer.
37
# Describe:
Procedure for **subtracting rational numbers**.
Ensure the **denominators** are the **same**, convert to equivalent fractions if necessary, then **subtract** the **numerators**.
## Footnote
The common denominator remains unchanged.
38
# Identify:
1/2 + 1/4 = \_\_\_\_
3/4
## Footnote
The LCD is 4, so 1/2 becomes 2/4.
39
# Explain:
How do you **reduce** a **rational number** to its **simplest form**?
**Divide** both the **numerator** and **denominator** by their **greatest common factor**.
## Footnote
Example: 10/20 reduces to 1/2.
40
# Explain:
How do **rational numbers** **differ** from **fractions**?
* **Rational numbers** can have **integers** as their numerator and denominator.
* **Fractions** can have **whole numbers** as their numerator and denominator.
## Footnote
All fractions are rational numbers, but not all rational numbers are fractions.
41
# Define:
greatest common factor
| (**GCF**)
The **greatest factor** that **two numbers** are both **divisible by**.
## Footnote
It is used to simplify rational numbers.
42
# Explain:
How to **multiply** two **rational numbers**.
**Multiply** the **numerators together** for the new numerator and the **denominators together** for the new denominator.
## Footnote
For rational numbers ab and cd, ab×cd = a×c / b×d.
43
# Explain:
The process of **simplifying** a **rational number**.
**Divide** **both** the **numerator** and the **denominator** by their **GCF**.
## Footnote
Example: To simplify 16/20, divide both by 4 to get 4/5.
44
# Define:
The **reciprocal** of a **rational number**.
It is the result of **flipping** the **numerator** and **denominator**.
## Footnote
For the rational number **ab**, the reciprocal is **ba**.
45
# Explain:
How to **divide** two **rational numbers**
**Multiply** the **first rational** number **by** the **reciprocal** of the **second rational** number.
## Footnote
For rational numbers ab and cd, ab÷cd = ab×dc.
46
# Explain:
Why does the **order** matter when **dividing rational numbers**?
Because **ab÷cd ≠ cd÷ab**.
## Footnote
This can lead to different results.
47
# Identify:
The **formula** for **dividing rational numbers**.
ab÷cd = a×d / b×c.
## Footnote
This involves keeping the first number and flipping the second.
48
# Define:
Estimate
A **quick guess** that is close enough to work with but **not necessarily accurate**.
## Footnote
Estimation is useful when strict accuracy is not required.
49
# Identify:
The most common way to **estimate.**
**Rounding** numbers.
## Footnote
Rounding helps simplify calculations by reducing complexity.
50
# Identify:
The magic **number** for **rounding**.
5
## Footnote
If the digit to the right of the desired rounded digit is 5 or higher, round up; otherwise, round down.
51
# Identify:
The **steps** to **round a number**.
1. Look at the digit to the right of the desired digit.
2. If 0-4, round down.
3. If 5-9, round up.
## Footnote
Following these steps ensures accurate rounding.
52
# Explain:
The purpose of **estimating sums**.
To **simplify** addition problems and quickly **gauge totals**.
## Footnote
Estimating sums can help in budgeting and checking calculations.
53
# Explain:
How should you **estimate** when dealing with **money**?
**Round** all values **up** to the **next higher whole dollar**.
## Footnote
This prevents underestimating total costs.
54
# Describe:
What is **estimating totals** with **multiplication** used for?
To estimate **counts** in a population **based on a sample**.
## Footnote
This method is useful when counting an entire population is impractical.
55
# Define:
Equivalent
When two or more quantities (or things) are **equal** in **value**.
56
# Identify:
What **forms** can **equivalent quantities** take?
* Number
* Fraction
* Decimal
* Percentage
57
# Define:
Equivalent fractions
**Fractions** that represent the **same** **ratio** or **value**.
58
# Describe:
The **role** of a **numerator** in a fraction.
**How many parts** are being used.
59
# Describe:
The **role** of a **denominator** in a fraction.
Number of **parts** into which a **whole** is **divided**.
60
# Explain:
How can you **verify** if **two fractions** are **equivalent**?
By cross-multiplication.
61
# Explain:
Cross-multiplication
The **product** of the **numerator** of the **first** fraction and the **denominator** of the **second** **equals** the **product** of the **denominator** of the **first** and the **numerator** of the **second**.
62
# Describe:
What does an **equivalent decimal** represent?
A **portion** of a **full value**, with a **whole number** part and a **decimal** part.
63
# Describe:
How to create an **equivalent decimal**.
By **adding zeros** to the end of the decimal.
64
# Describe:
The method for **converting decimals** into **fractions**.
**Determine** the **denominator** based on the **last digit's place value**.
65
# Explain:
How **whole numbers** can be represented **as fractions**.
By writing them **as the number over 1**.
## Footnote
e.g., 5 as 5/1
66
# Explain:
How to convert **percentages into fractions**.
Write the percentage as the numerator and 100 as the denominator.
67
# Identify:
The process of **converting a percentage** to a decimal.
Move the **decimal point 2 spaces** to the left.
68
# Define:
percent
Per one hundred.
## Footnote
A percent represents an **amount divided into 100** units.
69
# Describe:
What is a method for solving **percent** problems?
When you see a percent of something, **translate 'of' into multiplication**.
## Footnote
**Example**: 75 percent of 20 translates to 75% x 20.
70
# Explain:
What does "**a number out of another number**" translate to in mathematical terms.
Division
## Footnote
**Example**: 65 out of 80 translates to 65 / 80.
71
# Explain:
If a shoe costs **$218** and is **discounted by 55%**, what is the **amount paid** after the discount?
$98.10
## Footnote
Calculate 45% of $218 after determining the remaining percentage from the discount.
72
# Define:
ratio
A means to show **relative size** between **two or more** values.
## Footnote
Ratios compare values rather than giving actual amounts.
73
# Identify:
What are 4 different ways **ratios** can be written?
1. With a colon (e.g., 2:1)
1. With a forward slash (e.g., 2/1)
1. As a decimal (e.g., 2.0)
1. As a percentage (e.g., 200%)
## Footnote
The simplest form is often used for clarity.
74
# Identify:
What is the **simplest form** of the **ratio 4:20**?
1:5
## Footnote
For example, this could mean there are 5 birds for every tree.
75
# Define:
proportion
A statement that **two ratios** are **equal** to **each other**.
## Footnote
For example, 4:2 = 2:1.
76
# Identify:
What is the **ratio** of pink to blue to orange if 10 people like blue, 12 like pink, and 7 like orange?
12:10:7
## Footnote
This ratio is already in its simplest form.
77
# Identify:
**Represent** this recipe as a **ratio**: for every **1 cup** of sugar, **4 cups** of water are needed.
1:4 (sugar to water).
78
# Identify:
In a town with **400 commuters**, **120 drive** to work while **280 use bicycles**. What is the **ratio** of drivers to cyclists?
120:280
79
# Identify:
If car batteries and decorative garden gnomes sell in a ratio of **35:2**, how many gnomes are sold after selling **280 car batteries**?
16
## Footnote
This is found by setting up the proportion 35:2 = 280:g.
80
# Identify:
What **operation** is primarily used to **solve proportions**?
multiplication
## Footnote
This can be done vertically, horizontally or diagonally (cross-multiplication).
81
# Explain:
When is the **vertical method** best used while **solving proportions**?
When there is a **multiple between the quantities** in the same ratio.
## Footnote
Example: 3/9 = 5/x
Since 9 = 3×3, multiply 5×3 to get 𝑥 = 15
Here, the vertical method works because one term is a multiple of the other in the same ratio.
82
# Explain:
What is the **horizontal method** used for?
To **find** the **missing part** of **equivalent fractions**.
## Footnote
It is best used when there is a common multiple between the two numerators or denominators.
83
# Describe:
The **diagonal method** in solving proportions.
Also known as **cross-multiplication**; it involves taking the product of opposite numerators and denominators.
## Footnote
This method is useful when vertical or horizontal multiples are not easily recognizable.
84
# Identify:
The **formula** for a **proportional relationship**.
a/b = c/d
## Footnote
It can also be expressed as **a:b::c:d**.
85
# Define:
word problem
A math **problem expressed in English** rather than symbols.
## Footnote
Word problems often require translation into algebraic equations.
86
# Identify:
The **three methods** to **solve a proportion**.
1. Vertical
1. Horizontal
1. Diagonal (cross-multiplication)
## Footnote
Each method is suited for different types of proportions based on the relationships between the quantities.
87
# Identify:
The **three steps** in solving **word problems**.
1. **Visualize** the problem.
2. **Write** your equations.
3. **Solve** the equations.
88
# Define:
one-step **algebra equation**
An equation that requires only **one operation to solve**.
## Footnote
The operations can be addition, subtraction, multiplication, or division.
89
# Identify:
Common **operations** used in **one-step algebra equations**.
* Addition
* Subtraction
* Multiplication
* Division
## Footnote
These operations constitute the single step needed to solve the equation.
90
# Describe:
The **first step** in **translating a word problem**.
**Identify** and **highlight** **important** words and phrases.
## Footnote
Look for **numbers** and **operation indicators**.
91
# Explain:
What does "**less than**" imply in a word problem?
Indicates **subtraction** and can **reverse the order** of numbers.
## Footnote
For example, 'four less than a number' translates to 'number - 4'.
92
# Identify:
The correct translation of "**four less than a number equals eight**".
x - 4 = 8
## Footnote
The correct order is crucial; the larger number comes first.
93
# Explain:
How do you **isolate** the **variable** in the equation **x - 4 = 8**?
**Add 4 to both sides** of the equation.
## Footnote
This results in x = 12.
94
# Identify the equation:
Charles has **twice** the amount of dollars that Josh has.
C = 2 * J
## Footnote
C represents the dollars Charles has, and J represents the amount of dollars Josh has.
95
# Identify:
The **four steps** for solving **algebra word problems**.
1. **Analyze** the problem.
2. **Gather** information.
3. **Translate** into an equation.
4. **Solve** the equation.
## Footnote
These steps provide a structured approach to solving word problems.
Decks in class (16)
# Cards
-
1 - Analyzing and Understanding Literature94
-
2 - Literary Methods and Their Effects75
-
3 - Reading and Communication Skills115
-
4 - Number Sense and Basic Algebra95
-
5 - Geometry and Measurement Concepts118
-
6 - Data Analysis and Probability Skills74
-
7 - Historical Continuity and Geographic Regions103
-
8 - Socio-Historical Shifts: Effects of World-Changing Conflicts97
-
9 - Human Interaction with Nature, Resources, and the Earth's Physical Aspects78
-
10 - Civics, Government, and Economic Choices124
-
11 - Nature and History of Science110
-
12 - Physics130
-
13 - Chemistry and Biology152
-
14 - Ecology and Earth Science116
-
15 - Astronomy and Atmospheric Science70
-
16 - Science, Technology, and Social Perspectives89
