Question
2.1. Draw a diagram and use it to define and explain the three types of numbers: ordinal, cardinal, and nominal. 2.2. In the decimal number system, we can describe a number in different forms. Describe \( 5 \mathbf{4 0 5}, \mathbf{3 6 2} \) in words, in place value and in terms of the power of 10 . (6) 2.3. Design your own equation on distributive property and associative property. Explain how you will assist grade 4 learners to give solutions to each property.
Ask by Gibbs Wyatt. in South Africa
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
**2.1. Types of Numbers: Ordinal, Cardinal, and Nominal**
- **Cardinal Numbers:** Represent quantity (e.g., 5 apples).
- **Ordinal Numbers:** Indicate position or order (e.g., 3rd place).
- **Nominal Numbers:** Used for labeling or identification (e.g., jersey number 12).
**2.2. Describing the Number 5,405,362**
- **In Words:** Five million, four hundred five thousand, three hundred sixty-two.
- **In Place Value:**
- Millions: 5,000,000
- Hundred Thousands: 400,000
- Thousands: 5,000
- Hundreds: 300
- Tens: 60
- Ones: 2
- **In Terms of Powers of 10:**
\[
5,405,362 = 5 \times 10^6 + 4 \times 10^5 + 0 \times 10^4 + 5 \times 10^3 + 3 \times 10^2 + 6 \times 10^1 + 2 \times 10^0
\]
**2.3. Distributive and Associative Properties**
- **Distributive Property Example:**
\[
3 \times (4 + 5) = (3 \times 4) + (3 \times 5) = 27
\]
- **Teaching Strategy:** Use physical objects like blocks to demonstrate distributing multiplication over addition.
- **Associative Property Example:**
\[
(2 + 3) + 4 = 2 + (3 + 4) = 9
\]
- **Teaching Strategy:** Show that grouping numbers differently does not change the total sum using grouping circles or number lines.
**Summary:**
- **Cardinal:** Counts quantity.
- **Ordinal:** Shows order.
- **Nominal:** Identifies objects.
- **Distributive Property:** Allows multiplication over addition.
- **Associative Property:** Allows grouping in addition or multiplication without changing the result.
- **Teaching Methods:** Use concrete examples, visual aids, interactive activities, real-life scenarios, and practice problems to help Grade 4 learners understand these concepts effectively.
Solution
### **2.1. Types of Numbers: Ordinal, Cardinal, and Nominal**
**Definition and Explanation:**
1. **Cardinal Numbers:**
- **Definition:** Cardinal numbers represent *quantity*; they tell *how many* of something there are.
- **Examples:** 1, 2, 3, 10, 100.
- **Use:** Counting objects (e.g., "There are **5** apples.")
2. **Ordinal Numbers:**
- **Definition:** Ordinal numbers indicate the *position* or *order* of things in a series.
- **Examples:** 1st, 2nd, 3rd, 10th, 100th.
- **Use:** Describing rank or sequence (e.g., "She finished in **3rd** place.")
3. **Nominal Numbers:**
- **Definition:** Nominal numbers are used for *labeling* or *identifying* without indicating quantity or order.
- **Examples:** Phone numbers, jersey numbers, house numbers.
- **Use:** Identification purposes (e.g., "Her jersey number is **12**.")
**Diagram Explanation:**
Imagine a Venn diagram with three overlapping circles, each representing one type of number. However, in reality, these types are distinct and do not overlap. Here's a textual representation:
```
+-----------------+
| Cardinal |
| Numbers |
| (Quantity) |
+-----------------+
+-----------------+
| Ordinal |
| Numbers |
| (Position) |
+-----------------+
+-----------------+
| Nominal |
| Numbers |
| (Labeling) |
+-----------------+
```
**Visual Representation Suggestions:**
- **Cardinal:** Show a group of objects (e.g., 5 apples) with the number "5" indicating quantity.
- **Ordinal:** Show a race with runners labeled 1st, 2nd, 3rd.
- **Nominal:** Display a house with a number "12" on it for identification.
---
### **2.2. Describing the Number 5,405,362**
Let's break down the number \( 5,405,362 \) into different forms:
**a. In Words:**
- **Five million, four hundred five thousand, three hundred sixty-two.**
**b. In Place Value:**
Each digit in the number has a specific place value based on its position.
| Digit | Place Value | Value |
|-------|--------------------|---------------|
| 5 | Millions | 5,000,000 |
| 4 | Hundred Thousands | 400,000 |
| 0 | Ten Thousands | 0 |
| 5 | Thousands | 5,000 |
| 3 | Hundreds | 300 |
| 6 | Tens | 60 |
| 2 | Ones | 2 |
**c. In Terms of Powers of 10:**
Each digit can be expressed as a multiple of 10 raised to a certain power based on its position.
\[
5,405,362 = 5 \times 10^6 + 4 \times 10^5 + 0 \times 10^4 + 5 \times 10^3 + 3 \times 10^2 + 6 \times 10^1 + 2 \times 10^0
\]
**Explanation:**
- **Millions Place (10^6):** 5 × 1,000,000 = 5,000,000
- **Hundred Thousands Place (10^5):** 4 × 100,000 = 400,000
- **Ten Thousands Place (10^4):** 0 × 10,000 = 0
- **Thousands Place (10^3):** 5 × 1,000 = 5,000
- **Hundreds Place (10^2):** 3 × 100 = 300
- **Tens Place (10^1):** 6 × 10 = 60
- **Ones Place (10^0):** 2 × 1 = 2
---
### **2.3. Equations and Teaching the Distributive and Associative Properties**
**a. Distributive Property:**
**Equation Example:**
\[
3 \times (4 + 5) = (3 \times 4) + (3 \times 5)
\]
**Calculation:**
\[
3 \times 9 = 12 + 15 \implies 27 = 27
\]
**Explanation:**
The distributive property shows how multiplication interacts with addition. It allows us to multiply a number by a sum by multiplying each addend separately and then adding the products.
**b. Associative Property:**
**Equation Example:**
\[
(2 + 3) + 4 = 2 + (3 + 4)
\]
**Calculation:**
\[
5 + 4 = 2 + 7 \implies 9 = 9
\]
**Explanation:**
The associative property shows that the way numbers are grouped in addition or multiplication does not change their sum or product.
**c. Teaching Strategies for Grade 4 Learners:**
1. **Use Concrete Examples:**
- **Distributive Property:** Use physical objects like blocks. For example, if you have 3 groups of (4 blocks + 5 blocks), show that it's the same as having (3 groups of 4 blocks) plus (3 groups of 5 blocks).
- **Associative Property:** Use grouping with objects. Show that grouping 2 blocks and 3 blocks first, then adding 4 blocks, gives the same total as grouping 3 blocks and 4 blocks first, then adding 2 blocks.
2. **Visual Aids:**
- **Distributive Property:** Draw arrays or area models to represent the multiplication and distribution.
- **Associative Property:** Use number lines or grouping circles to visualize different groupings.
3. **Interactive Activities:**
- **Distributive Property:** Have students create their own examples using addition and multiplication, then apply the distributive property to solve.
- **Associative Property:** Engage students in rearranging groups of objects to see that the total remains the same.
4. **Relate to Real-Life Scenarios:**
- **Distributive Property:** Explain scenarios like distributing candies evenly among friends.
- **Associative Property:** Use examples like organizing items into different groupings without changing the total number.
5. **Practice Problems:**
- Provide a variety of problems where students can apply these properties.
- Encourage peer teaching where students explain their reasoning to each other.
6. **Use Stories or Games:**
- Incorporate simple stories where characters need to use these properties to solve problems.
- Create matching games where students match different expressions that represent the same value using these properties.
**Example Activity for Distributive Property:**
*Problem:* There are 3 baskets. Each basket has 4 red apples and 5 green apples. How many apples are there in total?
*Solution Using Distributive Property:*
\[
3 \times (4 + 5) = (3 \times 4) + (3 \times 5) = 12 + 15 = 27 \text{ apples}
\]
*Teaching Point:* Show students that multiplying the total number inside the parentheses by 3 gives the same result as multiplying each part separately and then adding them together.
**Example Activity for Associative Property:**
*Problem:* Calculate \( (2 + 3) + 4 \) and \( 2 + (3 + 4) \).
*Solution:*
\[
(2 + 3) + 4 = 5 + 4 = 9
\]
\[
2 + (3 + 4) = 2 + 7 = 9
\]
*Teaching Point:* Demonstrate that grouping the numbers differently does not change the total sum.
---
By using these explanations, examples, and teaching strategies, Grade 4 learners can grasp the concepts of ordinal, cardinal, nominal numbers, and understand the distributive and associative properties effectively.
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
Ordinal numbers are utilized to denote position or rank in a sequential order, such as "first," "second," or "third." You can visualize this with a race, where the competitors are numbered according to their finish positions. Cardinal numbers, on the other hand, represent quantity—like the number of apples in a basket—answering the question "how many?" Lastly, nominal numbers serve as labels or identifiers without any quantitative meaning, like jersey numbers in sports; they help categorize but don't indicate value. In the decimal number system, the number \( 5 4 0 5 \) can be articulated as "five thousand four hundred five." In terms of place value, it breaks down to \( 5 \times 1,000 + 4 \times 100 + 0 \times 10 + 5 \times 1 \). Therefore, in terms of the power of 10, we can express it as \( 5 \times 10^3 + 4 \times 10^2 + 0 \times 10^1 + 5 \times 10^0 \). Similarly, \( 3 6 2 \) is "three hundred sixty-two," represented as \( 3 \times 100 + 6 \times 10 + 2 \times 1 \), or \( 3 \times 10^2 + 6 \times 10^1 + 2 \times 10^0 \). For the distributive property, let's take the equation \( 3(4 + 5) \). To help fourth graders, I would first explain how to expand it: by distributing \( 3 \) to both \( 4 \) and \( 5 \), we get \( 3 \times 4 + 3 \times 5 \). Then, I would illustrate using visual aids or tangible objects to show how breaking down a number doesn't change its value. For associative property, we can use \( (2 + 3) + 4 \). I’ll teach them that it doesn’t matter how we group the numbers; they can also perceive it as \( 2 + (3 + 4) \). I’d engage them by having them group different items and add them up in both styles to see that they arrive at the same result.
