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- END UNIT 1 ASSIGNMENTOpened: Saturday, 27 May 2023, 12:00 PMDue: Monday, 29 May 2023, 12:00 AM
UNIT 10:Sequences that include whole numbers, fractions and decimals
10.1 Ordering whole numbers according to their size
in increasing order
Activity 10.1
1. Rwandan athletes participated in the national athletics trials. They
participated in the following races:
10 000 m, 800 m, 100 m, 200 m, 400 m and 5 000 m.
Arrange the races in order of increasing distance. Justify your answer.2. Discuss situations where you arrange quantities in increasing order.
Tip:
We can arrange numbers in increasing order. This is done by ordering/arranging them from the smallest to the largest.
Example 10.1
Describe how the following numbers can be arranged in increasing
order.
46 295, 45 690, 68 925
Solution
By checking the digits in the highest place value to the digits in the
lowest place value.
The numbers 46 295, 45 690, 68 925 arranged in increasing order are45 690, 46 295, 68 925.
Practice Activity 10.1
Arrange the numbers below in increasing order.
1. 5 000 m, 4 000 m, 9 000 m
2. 637 045, 705 365, 673 045, 637 450
3. 491 279, 137 004, 397 080, 491 792
4. 26 734, 62 374, 62 347, 63 437
5. 431 209, 413 209, 431 290, 413 029
6. 584 039, 548 039, 854 390, 458 309
Describe how to arrange the following in increasing order.
7. 783 165, 738 165, 783 615, 731 865
8. 627 558, 627 585, 672 558, 672 855
9. 97 862, 83 052, 78 962, 97 62810. 413 500, 431 500, 134 500, 351 400
10.2 Ordering whole numbers according to their size
in decreasing order
Activity 10.2
1. The table below shows the number of soccer fans who attended theCECAFA tournament. The data is for the first four matches.
• Which match had
(i) the lowest attendance?
(ii) highest attendance?
• Now arrange the match attendance in decreasing order. Justify
your answer.2. Tell examples where you can arrange quantities in decreasing order.
Tip:
We can arrange numbers in decreasing order. This is done by arrangingthe numbers from the largest to the smallest
Example 10.2
Explain how to arrange the following in decreasing order.
43 250, 42 420, 43 502, 40 352
Solution
By checking the numbers from the digit with the highest value to the
lowest value.
The numbers arranged in decreasing order are43 502, 43 250, 42 420, 40 352
Practice Activity 10.2
1. Arrange the following numbers in decreasing order.
(a) 213 456, 213 564, 213 546, 213 645
(b) 23 451, 23 514, 23 145, 23 415
(c) 860 720, 806 720, 860 270, 860 027
2. Arrange the following in decreasing order. Discuss your steps.
(a) 602 097, 632 097, 602 039, 600 397
(b) 708 540, 785 040, 780 504
(c) 234 567, 243 567, 235 467
3. Four farmers sold their farm produce. The money they got are recordedin the table below.
(a) Order the money of the four farmers in decreasing order.
(b) Which farmer got the highest amount of money. Explain youranswer.
10.3 Simple sequences that include fractions
Activity 10.3• Discuss the sequence given below and the pattern used.
• Write more numbers on flash cards with a pattern that follows 1 1/2 in
increasing order.
• Formulate more tasks on sequences with a pattern that follows 1 1/2
in increasing order.• Explain the pattern used.
Practice Activity 10.3
Find the next numbers in the sequences below.
Explain the steps involved in calculating the next numbers.
10.4 Simple sequences that include decimals
Activity 10.4
• Discuss the sequence given below and discover the pattern used.
10, 10.5, 11, 11.5, 12, 12.5, ___, ___
• Form your own sequences involving decimals. Make presentation tothe class.
Example 10.4
Find the next numbers in the sequence below.
5, 5.5, 6, 6.5, 7, 7.5, ___, ___
SolutionFind the difference in between the numbers.
The numbers are increasing by 0.5. Find the next number in the sequence
by adding 0.5 to 7.5. Then find the following number.
7.5 + 0.5 = 8
8 + 0.5 = 8.5
The next numbers in the sequence are 8 and 8.5. The sequence is5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5
Practice Activity 10.4
Find the next numbers in the sequences below.
1. 1, 1.5, 2, 2.5, 3, 3.5, 4, ___, ___
2. 14.5, 13, 11.5, 10, 8.5, 7, ___, ___
3. 2.5, 5, 7.5, 10, ___
4. 21, 21.5, 22, 22.5, 23, ___
Find the next number in the sequences below. Explain your steps.
5. 70, 73.5, 77, 80.5, 84, 87.5, ___, ___
6. 19, 18.5, 18, 17.5, 17, 16.5, 16 ___
7. 30, 30.5, 31, 31.5, 32, 32.5, ___
8. 90, 90.5, 91, 91.5, 92, 92.5, ___, ___
9. 80, 80.5, 81, 81.5, 82, 82.5, ___, ___
10. 50, 50.5, 51, 51.5, 52, 52.5, ___
10.5 Sequence with constant differences
Activity 10.5
• Discuss the sequence given. Discover the pattern used and find the
next number.
25, 28, 31, 34, 37, ___
• Now, form your own sequences with constant differences. Then makea presentation to the class.
Tip: Sequences with constant differences are called arithmetic progressions.
Example 10.5
Express the steps involved in getting the next number in the sequence
below.2, 4, 6, 8, _____
Solution
Method 1
Steps: • Find the difference between two consecutive numbers.• Observe the pattern of the differences.
Observation: The difference is 2. Therefore we add 2 to 8. So, 8 + 2 = 10
The sequence is 2, 4, 6, 8, 10.
Method 2
We find the missing number using a number line.On a number line, we have;
Moving in +2 steps. The pattern is 2, 4, 6, 8, 10.
Practice Activity 10.5
Find the missing numbers in the sequences below.
1. 35, 37, 39, 41, 43, ___, ___
2. 7, 11, 15, 19, 23, ___, ___
3. 20, 25, 30, 35, 40, ___, ___
4. 70, 74, 78, 82, 86, ___, ___
5. 25, 28, 31, 34, 37, ___, ___
Find the mising numbers in the sequences below. Explain your steps.
6. 40, 43, 46, 49, ___, ___
7. 60, 64, 68, 72, ___
8. 2, 5, 8, 11, 14, ___
9. 52, 57, 62, 67, ___, ___10. 22, 28, 34, 40, 46, ___
10.6 Sequences with constant ratios
Activity 10.6
Look at the sequences given below.
(a) 1, 2, 4, 8, 16, ___, ___, ___ (b) 3, 9, 27, 81, ___
(i) Find the missing numbers.
(ii) Describe the pattern you have discovered.
(iii) Form your own sequences with the pattern you discovered. Thenmake a presentation to the class.
Tip: We can have a sequence with constant ratios. These are called geometricprogressions.
Example 10.6
Discuss the steps involved to extend the sequences below.
5, 15, 45, ___
Solution
Find the constant ratio by dividing each number by the previous one.
15/5= 45/15= 3
The constant ratio is 3. Multiply 45 × 3 = 135Therefore the sequence is 5, 15, 45, 135.
Practice Activity 10.6
Find the next numbers in the following sequences.
1. 1, 2, 4, 8, ___, ___ 2. 16, 32, 64, ___
3. 3, 9, 27, 81, ___ 4. 4, 16, 64, ___
Find the missing numbers in the sequences below. Explain your steps.
5. 1, 5, 25, 125, ___ 6. 10, 100, 1 000, ___
7. 176, 88, 44, 22, ___, ___ 8. 2, 8, 32, ___, ___9. 3, 27, 243, ___ 10. 6, 12, 24, ___, ___
10.7 Sequences with regularly changing differences
Activity 10.7
• Discuss the patterns in the sequences below. Find the next numbers
in the sequences.
(i) 1, 3, 6, 10, 15, ___ (ii) 4, 5, 8, 14, 24, ___
What do you notice?
• Study the sequence: 2, 3, 5, 7, 11, ___, ___. Explain the rule used infinding the sequence and make a presentation
Example 10.7
Describe the steps involved to find the next numbers in the sequence
below.
2, 3, 6, 12, 22, ___, ___
Solution
Steps: • Find the difference between two consecutive numbers.• Observe the pattern of the differences.
Observation: The difference is increasing. Numbers added to get
difference has number added greater by 1 than previous.
That is we add 2, then 3, then 4. So add 5, then 6 asshown.
Thus, the sequence is: 2, 3, 6, 12, 22, 37, 58.
Practice Activity 10.7
Find the next numbers in the sequences below.
1. 1, 4, 10, 19, ___, ___
2. 12, 13, 16, 22, 32, ___, ___
3. 50, 52, 55, 59, ___, ___
4. 8, 11, 15, 20, 26, ___, ___
Discuss the patterns in the sequences below. Then find the missing numbers.
5. 20, 23, 27, 32, 38, ___
6. 70, 75, 81, 88, 96, ___, ___
7. 31, 32, 35, 41, 51, ___
8. 44, 45, 48, 54, 64, ___
9. 62, 63, 66, 72, ___10. 100, 101, 104, 110, 120, ___
10.8 Sequences where the difference is geometric
Activity 10.8
• Look at the sequence: 11, 23, 47, 95, ___.
• Find the difference between consecutive numbers. What pattern is
the difference? Explain your steps.
• Now, find the next number.
11, 23, 47, 95, ___
• Form your own sequences like the sequence above. Make postersfor your sequences and present to the class.
Example 10.8
Find the next number in the sequence below. Explain your steps.10, 21, 43, 87, ___
Solution
Steps:
• Find the difference between consecutive numbers.
• Observe the pattern of the differences.• Find the next number using the pattern.
The difference follows a geometric pattern. The next difference is
44 × 2 = 88.
So add 88 + 87 = 175.
Thus, the sequence is:10, 21, 43, 87, 175.
Practice Activity 10.8
Find the next numbers in the sequences below.
1. 1, 3, 7, 15, ___ 2. 2, 5, 11, 23, ___, ___
3, 3, 7, 15, 31, ___, ___ 4. 6, 13, 27, 55, ___
5. 12, 25, 51, 103, ___
Find the next number in the sequences below. Discuss your steps and
present.
6. 5, 11, 23, 47, ___ 7. 8, 17, 35, 71, ___
8. 20, 41, 83, 167, ___ 9. 7, 15, 31, 63, ___10. 4, 9, 19, 39, ___
Revision Activity 10
1. Arrange the following from the smallest to the largest.
(a) 2 300, 3 200, 2 003, 3 002
(b) 5 732, 7 532, 7 352, 5 372
2. Arrange the following in decreasing order.
(a) 9 481, 9 841, 9 148, 9 099
(b) 23 452, 23 425, 23 245, 25 254
(c) 11 000, 10 100, 10 010, 10 001
3. Find the next number in the sequence below. Explain your steps.
4. Use a number line to find the next number in the following sequences.
Explain your pattern.
(a) 3, 6, 9, 12, ___ (b) 1, 5, 9, 13, ___
5. Use geometric patterns to determine the next number in the
sequences below. Discuss your patterns.(a) 1, 4, 9, 16, ___ (b) 3, 7, 11, 15, ___
Word list
Sequence Fractions Decimals
Increasing Decreasing Constant ratios
Geometric difference
Task
Do the following.
(i) Read each word aloud to your friend.
(ii) Write the meaning of each of the words above. Discuss with your friend.(iii) Write sentences using each of the words above. Read with your friend.