Classifying whole numbers as odd and even in different situations

Subsection 1.1.1 Classifying whole numbers as odd and even in different situations

Teacher Resource 1.1.3.

To assist your teaching, we have prepared lesson resources, aligned with this textbook and the CBC. These include general lesson plans and detailed step-by-step lesson guides. Depending on whether your students will be able to access online content on devices such as laptops, computers or phones during class, you can choose a resource from below to assist you in your teaching.

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My learners do not have access to devices during class:

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My learners have access to devices during class:

Offline step-by-step guide

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Online step-by-step guide

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Activity 1.1.1.

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Working in groups, write numbers from \(1\) to \(50\text{.}\)
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Recall: What is an odd number? What is an even number?
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Sort the numbers you wrote down into odd or even.
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What patterns do you notice between even and odd numbers?
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Discuss how a number is classified.
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Brainstorm a real life example where you can find odd and even numbers e.g pairs of shoes are even numbers.
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Describe why classifying numbers in real-life could be useful.
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Share your work with your fellow learners.
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Key Takeaway 1.1.4.

Even numbers are numbers that are divisible by \(2\text{.}\)

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Odd numbers are numbers that when divided by \(2\text{,}\) you get a remainder.

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Properties

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The sum or difference of two even numbers is even.
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Example: \(6 + 4 = 10\) and \(6-2 = 4\text{.}\)
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The sum or difference of two odd numbers is even.
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Example: \(7+3 = 10 \) and \(11-9 = 2\)
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The sum or difference of an even and an odd number is always odd.
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Example: \(8+ 5 = 13\) and \(8-5 = 3\)
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When two odd integers are multiplied, the result is always an odd number.
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Example: \(3 \times 3 = 9\)
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When two even integers are multiplied, the result is an even number.
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Example: \(12 \times 12 = 144\) \(\)
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An even number multiplied by an odd number equals an even number.
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Example: \(12 \times 3 = 36\)
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Remark 1.1.5.

We can only talk about even and odd numbers if they are integers (like \(1, 2, 3, 4\)). Non-integers (like \(3.2\) or \(3.14159\ldots\)) are neither even nor odd.

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Criterion 1: How to Identify Even or Odd Integers

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A number is even if it ends with one of the digits: \(0, 2, 4, 6, 8. \)

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A number is odd if it ends with one of the digits: \(1, 3, 5, 7, 9.\)

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Example 1.1.6.

Classify the following numbers as even or odd:

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\(\displaystyle 1107\)
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\(\displaystyle 2028\)
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\(\displaystyle 3333\)
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\(\displaystyle 5052\)
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\(\displaystyle 1800\)
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\(\displaystyle 1349\)
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Solution.

\(1107\) is an odd number since its last digit is \(7\text{.}\)
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\(2028\) is an even number since its last digit is \(8\text{.}\)
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\(3333\) is an odd number since its last digit is \(3\text{.}\)
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\(5052\) is an even number since its last digit is \(2\) .
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\(1800\) is an even number since its last digit is \(0\text{.}\)
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\(1349\) is an odd number since it ends with \(9\text{.}\)
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Example 1.1.7.

Kirui has 35 cows on his farm and wants to group them into 2 pens. Will each pen have an equal number of cows? Explain using properties of even and odd numbers.

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Solution.

First we identify whether \(35\) is even or odd.

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Since the last digit is \(5\text{,}\) this makes \(35\) an odd number.

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Since an odd number cannot be divided evenly into equal groups, the cows can only be divided into two groups: one with \(18\) cows and the other with \(17\) cows. Therefore, the cows cannot be shared evenly across all pens.

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Checkpoint 1.1.8. Classifying Numbers as Even or Odd.

Load the question by clicking the button below.

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Exercises Exercise

1.

Classify the following numbers as even or odd using the given criterion.

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\(\displaystyle 1008\)
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\(\displaystyle 1521\)
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\(\displaystyle 2117\)
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\(\displaystyle 625\)
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\(\displaystyle 14\)
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\(\displaystyle 1703\)
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\(\displaystyle 9272\)
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\(\displaystyle 22801\)
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Answer.

\(1008\) is an even number.
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\(1521\) is an odd number.
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\(2117\) is an odd number.
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\(625\) is an odd number.
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\(14\) is an even number.
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\(1703\) is an odd number.
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\(9272\) is an even number.
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\(22801\) is an odd number.
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2.

List all the numbers between \(8102\) and \(8130\) and identify odd and even number from the range.

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Answer.

Even numbers: \(8104, 8106, 8108, 8110, 8112, 8114, 8116, 8118, 8120, 8122, 8124, 8126, 8128\text{.}\)

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Odd numbers: \(8103, 8105, 8107, 8109, 8111, 8113, 8115, 8117, 8119, 8121, 8123, 8125, 8127, 8129\text{.}\)

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3.

Find the sum of the first \(20\) numbers and determine if the result is odd or even.

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Answer.

The sum of the first \(20\) natural numbers is \(210\text{,}\) which is an even number.

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4.

A grade \(10\) class has \(52\) students and their class teacher wanted to group them in pairs. Will each group have an equal number of students? Explain using odd or even properties.

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Answer.

Since \(52\) is an even number, it can be divided evenly into pairs.

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