1. Many responses can make sense. For example, the number of seats could be an answer. It would also be correct to say that, since this plane isn’t going anywhere, not everyone needs to have a seat. More people could squeeze into it depending on how big everyone is. Ask your child, “How do you know?” and listen to their reasoning. Does it make sense? If so, then the answer is correct.
2. Your car might be going slower, faster, or exactly equal to 70 MPH on the freeway, depending on the speed limit.
3. A good rule of thumb is to double the length of the runway used for takeoff when calculating the length needed for landing. So if the plane touched down on Ludington Avenue near the waterfront, it would stop by the time it got to the House of Flavors.
4. It would need a longer runway in Denver. Because Denver’s airport is at a higher elevation, the air is less dense. “Thinner” air creates less lift, which means the plane must be going faster to take off.
1. Answers will vary. Listen for a convincing justification.
2. This problem is about multiplication. Four lines of 3 blue pegs each equals 12 blue pegs. Four lines of 4 green pegs each equals 16 green pegs.
3. Four, 9, and 16 are square numbers. You can make squares of pegs only using square numbers. Therefore, 25 pegs will also make a square.
4. To begin, you will use six pegs to make the 3 x 2 rectangle. When you double each side, you increase the rectangle’s size by a factor of 2 squared, which is 4. If you triple each side, you increase the area by a factor of 3 squared, which is 9.
1. There are 11 pirates.
2. One correct answer is two windows. Another correct answer would double this number to account for the other side of the ship. Most importantly, does your child give a sensible answer to the question, “How do you know?”
3. Correct answers will vary. The point of this question is for your child to explain their reasoning in a way that makes sense.
4. If you took this actual “ship” out of the museum and put it in the water, it would sink. But real pirate ships sailed across oceans, so crossing Lake Michigan could be possible. Every year dozens of sailboats make it around the world.
1. The wall is 8 feet tall, but the highest foothold is 42″ off the ground. How high you’ll be depends on what you think of as the highest point.
2. Counting each handhold (there are 87) is one way to answer this question. Your child might also choose to estimate. Here are some questions to encourage their thinking: What are minimum and maximum numbers that make sense? What strategy can you use to make an educated guess?
3. Correct answers will vary. Your child might start by estimating how long it would take to move a fraction of the distance and then multiply the fraction to get a total. Next, they might choose to multiply that total by 10 to get the amount of time it takes to complete 10 crossings. Their answer might account for the times to grow shorter (practice reduces each crossing time) or longer (fatigue increases each crossing time).
4. You might start by asking your child to guess what the tallest buildings in Ludington and Chicago are. As of 2022 they are the Longfellow Towers (85 feet) and the Willis Tower (1,450 feet). Dividing them by 200 means you could get to the top of the Longfellow Towers in less than one pitch. It would take 7.25 pitches to reach the top of the Willis Tower.
1. You should buy three more apples.
2. You can also divide the bananas evenly between three people.
3. You will pay $6.00 for two 12 oz. boxes (24 oz. total), which is less than $6.25. So the first option is cheaper. You can use a calculator to solve this problem, but doing it in your head is more challenging. Is there a way your child can use their knowledge of numbers to estimate the better option?
4. Correct answers will vary based on what meal your child chooses and how big their family is. Listen to their explanations and be certain you can honestly say, “I understand your thinking.”
1. Correct answers will vary.
2. There are four bubbles left.
3. Correct answers will vary. The goal of this question is to build an understanding of “bigger” and “smaller.” How does your child define those terms?
4. Six bubbles that are each two inches in diameter lined up side by side make one foot The cube would have 6 x 6 x 6 bubbles, or 36 x 6 = 216 bubbles.
1. There are now seven animals in the waiting room.
2. The patients are 57% dogs, 43% cats, and 0% other animals.
3. The vet can spend 10 minutes with each pet.
4. A dog has a higher body temperature than a human. The average human body temperature is 98.6°.
1. Correct answers will vary. One possible answer is that, because the pupil is inside the iris, the iris must be bigger. However, your child could also correctly say that the pupil is bigger because it takes up more surface area.
2. The goal of this question is for your child to develop a strategy for estimating. How can they determine the number of something they might not be able to count? If their reasoning makes sense, the answer can be considered correct. (If your child wants to count each individual eyelash, that’s fine, too!)
3. A person with 20/200 vision can see at 20 feet what the average person can see at 200 feet. Other ways of describing this answer can be correct as well. For example, a sign that’s 20 feet away for a person with 20/200 vision will be as clear as a sign will be at 200 feet away for a person with 20/20 vision.
4. Correct answers will vary. One possible response could begin with an estimate that this eye is close to seven feet tall. Because the average human eye is 0.93 inches in height, this eye is 78 times bigger. A giant who is 78 times taller than an average person would be about 432 feet tall!
1. There are 14 apples. Ten are left after eating four.
2. It will take four days.
3. The first question depends on a number of factors, such as how big you and your friend are and how much food each one of you has already eaten. The second question is asking your child to deconstruct the sum of 10 into two numbers: 0 + 10, 1 + 9, 2 + 8, 3 + 7, etc.
4. This is a trick question, because chimney swifts pairs do not nest with other pairs. Let’s pretend that we don’t know that, though. To figure out the answer, assume that each chimney swift nest is about four inches wide. If the perimeter of the silo is six feet, then 18 nests can fit in one level of the silo. How many levels of nests does your child think the silo can hold?
1. You have nine cows.
2. You have 54 cows.
3. Correct estimates will vary. Your child might start by estimating how much milk their family uses, then multiply that total by the number of families in the neighborhood. For further exploration, you can ask your child to define what a neighborhood is. Is their family a typical representation of it?
4. According to the US Department of Agriculture, this statement is true. Nevertheless, if you child says this statement is false and can explain why, their answer could be considered correct, too.
1. The bridge can hold two more trucks.
2. There are seven hats left on the wall. Some examples of correct answers are (1) five red and two blue, (2) three red and four blue, and (3) two red and five blue. For further exploration, ask your child for some answers that are not correct, such as four red and one blue.
3. You need four dump trucks.
4. Correct answers will vary, but, in general, more bricks should create a more stable tower. Listen for your child’s reasoning to make sense to you.
1. There are six people in your band.
2. The correct answer could be either 30 beats per minute or 120 beats per minute. How does your child define double or half of their rhythm? For example, if half means dividing the total number of notes in half, then the correct answer will be 30 beats per minute. If half means the time between taps is half, then it’s 120 beats per minute.
3. To most people, adjacent keys do not sound good together because their wavelengths interfere with each other. Many possible “rules” can work. The key is for your child to be able to describe their rules to explain their thinking.
4. There is one way to press zero strings, four ways to press a single string, six ways to press two strings, four ways to press three strings, and one way to press four strings. The total number of ways to press the strings is 16.