Replace Each Star by a Digit to Make the Equation True
Nicole Miller
Brainteaser # 1
, 4 X 7 = 6,743, 56
Replace each star by a digit to make the equation true.
To Solve:
- Trial and Error: Place digits 0-9 into the star of the answer.
- The answer to a multiplication problem can be divided by one of the factors to equal the other factor. Divide 6,743,056 (0 as the star) by 7 and see if the answer has a 4 in the hundreds place. Do this with the digits 1-9 as the star until your answer has a 4 in the hundreds place.
- Through Trial and Error, I came to solve the equation.
Answer:
963,408 X 7 = 6,743,856
Math Content:
Division (6,743,856 / 7 = 963,408) and Multiplication 963,408 x 7 = 6,743,856)
Conceptual Understanding:
The knowledge that the answer to a multiplication problem can be divided by one of the factors to equal the other factor.
Problem Solving Strategies:
What do you notice?
There is a 4 in the hundreds place in the unknown factor.
There is a missing number in the answer.
7 is very important.
What is the most critical place?
The star in the answer and the 4 in the factor of stars are the most critical places. This tells us that what we really need to look for.
ORKing
Keep track of which numbers you use to plug in for trial and error.
Keep your division problems neat and orderly to see which quotient has a 4 in the hundreds place.
Grade Level: 3rd
Differentiated Problem:
Smaller numbers:
4 X 2 = 4
What Next?
The numbers in each line below form a series. Write the next two numbers in each series.
24232128272532______
To Solve:
- Find the relationships between each number.
- 24 – 1 = 23, 23 – 2 = 21, 21 + 7 = 28, 28 – 1 = 27, 27 – 2 = 25, 25 + 7 = 32.
- Find the pattern. Between the numbers the pattern subtracts 1, then subtracts 2, and then adds 7. It repeats this in a pattern.
- From the last number, I subtracted 1 to solve the first _____, and then subtracted 2 to solve the second ____.
Answer:
242321282725323129
Math Content:
Addition (21 + 7 = 28) and Subtraction (24 – 1 = 23)
Conceptual Understanding:
The knowledge of addition and subtraction and understanding that patterns exist and being able to find them.
Problem Solving Strategies:
What do you notice?
There is some sort of pattern between these numbers.
ORKing
Keep track of the relationship between each number.
Grade Level: 1st and 2nd
Differentiated Problem:
Smaller numbers:
43187512______
Create Equality
Make an equation out of all the numbers and arithmetic signs in each line, using each number and sign only once.
3 3 3 3 81 = x x /
To Solve:
- Trial and Error: Experiment with the numbers and the signs.
- 81 has to be the number that is going to be divided because it is so high compared to the other numbers.
- Trial and Error solves the problem.
Answer:
81 / 3 = 3 x 3 x 3
27 = 27
Math Content:
Division (81 / 3 = 27) and Multiplication (3 x 3 x 3 = 27)
Conceptual Understanding:
The knowledge of division and multiplication and understanding their uses and the order of operations is very important.
Problem Solving Strategies:
What do you notice?
81 has to be the number that is going to be divided because it is so high compared to the other numbers.
What is the most critical place?
The 81 / 3 is the most critical place because it sets the answer of 27.
ORKing
Keep track of math computation.
Multiple Ways
81 / 3 x 3 = 3 x 3
Grade Level: 3rd
Differentiated Problem:
Addition:
3 3 3 3 = + +
3 + 3 = 3 + 3
6 = 6
Build the Box
To Solve:
- Visualize the geometric figure.
- Look for marks that would be in the right places.
- Pick the correct answer of the multiple choices.
Answer:
C.
Math Content:
Geometry, Shapes, and Patterns
Conceptual Understanding:
The visualization of geometric shapes and patterns is important.
Problem Solving Strategies:
What do you notice?
I notice the colored rectangle on the figure and the X with a circle on one of the sides.
What is the most critical place?
The colored rectangle and the X with a circle are very critical.
Multiple Ways
Physically build the figure.
Grade Level: 2nd
Differentiated Problem:
Addition:
Physically build the figure.
Toothpicks Will Do!
To Solve:
- Trial and Error.
- The use of the sides of the whole problem can manipulate the answer.
- Trial and Error solves the problem.
Answer:
Math Content:
Geometry
Conceptual Understanding:
The geometry of squares and rectangles help understand this problem.
Problem Solving Strategies:
What do you notice?
The sides of the whole rectangle are very important. One toothpick removed from the center bottom can remove an entire square.
What is the most critical place?
The sides are the most critical place.
ORKing
Trial and Error building with toothpicks and visualization.
Multiple Ways
Physically building with toothpicks.
Grade Level: 2nd
Differentiated Problem:
Physically building with toothpicks.