- Look at the figure. The rectangle is cut into equal squares. The numbers show how many squares are shaded in each row. How many should be shaded in Row 4 to keep the decrease pattern?
Answer: 2
Row counts: 8,6,4,?. Decrease by 2 each row, so 4−2=2. Option A. 3,4,5 break pattern.
- Look at the number sentence: 6 + ___ = 4 + 8. What number makes this sentence true?
Answer: 6
First, solve the right side: 4 + 8 = 12. So the equation becomes 6 + ___ = 12. To find the missing number, subtract: 12 - 6 = 6.
- What number makes this true? 13−?=6+4
Answer: 3
The right side is 6 + 4 = 10, so you need 13 minus a number to equal 10. That number is 3. A tempting mistake is 10 if you just use the sum from the right side, but 13 - 10 equals 3, not 10.
- What missing number makes this true? ?+4=9−2
Answer: 3
Start with the right side: 9 - 2 = 7. So the missing number plus 4 must equal 7, meaning ? + 4 = 7. That makes the missing number 3, because 3 + 4 = 7. A tempting wrong answer is 7, but 7 is the total after subtraction, not the number you need to add to 4.
- Emma has 8 stickers. She gives away some stickers and has 3 left. Then her friend gives her 4 more stickers. How many stickers did Emma give away?
Answer: 5 stickers
When you see a word problem with multiple steps, it's important to work through each part carefully and identify what the question is actually asking for.
Let's trace through Emma's stickers step by step. Emma starts with 8 stickers. After giving some away, she has 3 left. To find how many she gave away, you subtract: 8−3=5 stickers given away. The information about her friend giving her 4 more stickers afterward doesn't change how many she originally gave away.
Choice A (3 stickers) represents how many Emma had left after giving some away, not how many she gave away. This is a common trap where students confuse the remaining amount with the amount removed.
Choice B (4 stickers) is the number her friend gave her later. This information appears at the end of the problem, but it's unrelated to the question being asked.
Choice C (7 stickers) might come from incorrectly adding or subtracting the numbers in the problem without following the logical sequence.
Choice D (5 stickers) is correct because 8−3=5, showing that Emma must have given away 5 stickers to go from 8 down to 3.
When solving multi-step word problems, identify what the question is asking for first, then work through only the information you need to answer that specific question. Extra information in the problem might not be relevant to what you're solving for. - Tom arranges blocks in groups. The first group has 1 block, the second group has 3 blocks, the third group has 5 blocks. If this pattern continues, how many blocks will be in the sixth group?
Answer: 11 blocks
When you see a pattern problem like this, you need to look for the rule that connects each step. Let's examine how Tom's block groups are growing.
The pattern shows: 1 block, 3 blocks, 5 blocks. Notice that each group has an odd number of blocks, and they're increasing by 2 each time: 1+2=3, then 3+2=5. This tells us we're adding 2 blocks to get each next group.
Following this pattern: Group 4 would have 5+2=7 blocks, Group 5 would have 7+2=9 blocks, and Group 6 would have 9+2=11 blocks.
Looking at the answer choices: A) 11 blocks is correct because it follows our pattern perfectly. B) 10 blocks would break the pattern of odd numbers - every group in this sequence must have an odd number of blocks. C) 12 blocks also breaks the odd number pattern and would represent adding 3 blocks instead of 2. D) 13 blocks maintains the odd pattern but represents adding 4 blocks, which doesn't match the consistent increase of 2.
You can also think of this as the sequence of odd numbers: 1st odd number is 1, 3rd odd number is 5, 5th odd number is 9, and the 6th odd number after 1 is 11.
For pattern problems, always identify what stays the same and what changes between steps. Here, the "add 2" rule and the odd numbers both stayed consistent, making the pattern predictable. - Alex arranges chairs in rows. Row 1 has 4 chairs, Row 2 has 6 chairs, Row 3 has 8 chairs. If he continues this pattern, how many chairs will Row 6 have?
Answer: 14 chairs
Each row has 2 more chairs than the previous row. Row 1: 4, Row 2: 6 (+2), Row 3: 8 (+2). Continuing: Row 4: 10, Row 5: 12, Row 6: 14 chairs.
- Maya has twice as many marbles as Jake. Jake has 7 marbles. How many marbles does Maya have?
Answer: 14 marbles
If Maya has twice as many marbles as Jake, and Jake has 7 marbles, then Maya has 2 × 7 = 14 marbles.
- Look at this growing pattern: Week 1 has 2 flowers, Week 2 has 5 flowers, Week 3 has 8 flowers. How many flowers will there be in Week 5?
Answer: 14 flowers
When you see a growing pattern question, you need to figure out the rule that connects each step to the next. Look at how the numbers change from week to week.
Let's examine the pattern: Week 1 has 2 flowers, Week 2 has 5 flowers, Week 3 has 8 flowers. To find the rule, subtract each week's number from the next week's number. From Week 1 to Week 2: 5−2=3. From Week 2 to Week 3: 8−5=3. The pattern adds 3 flowers each week!
Now you can continue the pattern. Week 4 would have 8+3=11 flowers. Week 5 would have 11+3=14 flowers. This confirms that A) 14 flowers is correct.
Looking at the wrong answers: B) 13 flowers might come from miscounting or adding 2 instead of 3 somewhere in your calculation. C) 15 flowers could result from adding 4 instead of 3, or from skipping a step in your counting. D) 16 flowers is too high and might come from adding 3 twice to Week 3 instead of working step by step.
Remember this strategy for pattern questions: always find the difference between consecutive terms first. Once you know how much the pattern grows each time, you can confidently extend it to find any missing number. Write out each step to avoid counting errors. - What number makes this true? ?−3=8−5
Answer: 6
First work out the right side: 8 - 5 = 3. So the missing number minus 3 must also equal 3, and 6 - 3 = 3. The tempting wrong choice is 3, because it is the result of 8 - 5, but that is not the number you start with.
- Which number makes both true? ?+3=8,?−2=3
Answer: 5
To make ? + 3 = 8, you need 5 because 5 + 3 = 8. Then check the second statement: 5 - 2 = 3, so 5 works for both. The number 2 is tempting because it appears in the subtraction, but 2 - 2 is 0, not 3.
- Refer to the picture graph below. How many cupcakes should the empty box show to keep the doubling pattern?
Answer: 16
The picture shows rows with 2,4,8 cupcakes—each row doubles. Doubling 8 gives 16. Option C is correct. 12 and 14 are too low; 18 is higher than a double.
- Based on the bar graph shown, how many books should be in Thursday's bar to continue the pattern?
Answer: 8
The bars rise by 1 each day: Monday 5, Tuesday 6, Wednesday 7. Following the pattern, Thursday should be 8 books. 6 or 7 repeat earlier values; 9 skips the pattern.
- Sarah counts by 3s starting from 5: 5, 8, 11, 14, ___. What number comes next in her counting pattern?
Answer: 17
Sarah adds 3 to each number: 5+3=8, 8+3=11, 11+3=14, so 14+3=17. She's counting by 3s, so each number increases by exactly 3.
- What number belongs in both boxes? ?+?=8+2
Answer: 5
The right side is 8 + 2, which equals 10. Both boxes hold the same number, so you need a number added to itself to make 10. Since 5 + 5 = 10, the number is 5. The tempting wrong answer is 10 because it is the value of 8 + 2, but 10 + 10 is 20, not 10.
