4th Grade Common Core Math Tests with Answer Keys covering various standards.

The image shows two answer keys for 4th Grade Common Core Math tests. Below, I will explain the solutions for a few selected problems from each test to demonstrate how they are solved.

---

Test 3 (Left Side)

#### Problem 1.a: What is the value of 5 in 4,581,936?
- Solution: The digit "5" is in the hundred-thousands place.
- Value = \( 5 \times 100,000 = 500,000 \)
- Answer: 500,000

#### Problem 2.b: Compare the numbers below using >, <, or =.
- Numbers: 65,837 and 65,738
- Solution: Compare the digits from left to right:
- Both numbers start with 65.
- Next, compare the hundreds place: 8 > 7.
- Therefore, 65,837 > 65,738.
- Answer: \( 65,837 > 65,738 \)

#### Problem 3.a: Write a comparison statement to match the multiplication equation.
- Equation: \( 10 \times 8 = 80 \)
- Solution: This means 10 groups of 8 are equal to 80.
- Answer: "10 groups of 8 is equal to 80."

#### Problem 4.b: A librarian received 8 new science textbooks and 8 math textbooks. It took him 3 minutes to label and scan each book into the system. How long did it take him to label and scan all the new textbooks into the system?
- Solution:
- Total books = 8 (science) + 8 (math) = 16 books.
- Time per book = 3 minutes.
- Total time = \( 16 \times 3 = 48 \) minutes.
- Answer: 48 minutes

#### Problem 5.a: During a math test in class, Jessica finished 2/5 of the test within the first ten minutes. She was able to finish 1/5 of the test within the next five minutes. How much of the test did Jessica finish within the first fifteen minutes?
- Solution:
- Test completed in first 10 minutes = \( \frac{2}{5} \).
- Test completed in next 5 minutes = \( \frac{1}{5} \).
- Total completed = \( \frac{2}{5} + \frac{1}{5} = \frac{3}{5} \).
- Answer: \( \frac{3}{5} \) of the test.

#### Problem 7.a: Draw a shape with at least one right angle and acute angles.
- Solution: A triangle with one right angle and two acute angles is a right triangle.
- Answer: Draw a right triangle.

#### Problem 9.a: The perimeter of Steve's rectangular flower garden is 30 feet. If the width of the garden is 4 feet long, what is the length of Steve's flower garden?
- Solution:
- Perimeter formula for a rectangle: \( P = 2(L + W) \).
- Given: \( P = 30 \), \( W = 4 \).
- Substitute values: \( 30 = 2(L + 4) \).
- Simplify: \( 30 = 2L + 8 \).
- Solve for \( L \): \( 2L = 22 \) → \( L = 11 \).
- Answer: 11 feet

---

Test 8 (Right Side)

#### Problem 1.a: Write 435,018 in word form.
- Solution:
- 435,018 = Four hundred thirty-five thousand eighteen.
- Answer: Four hundred thirty-five thousand eighteen.

#### Problem 2.a: The soccer team players drank 12,350 mL of water after the first half of their game. After the second half, they drank 6,275 mL of water more than they did after the first half. How much water did they drink after the second half?
- Solution:
- Water after the first half = 12,350 mL.
- Additional water after the second half = 6,275 mL.
- Total water after the second half = \( 12,350 + 6,275 = 18,625 \) mL.
- Answer: 18,625 mL

#### Problem 3.a: Laura bought 6 bags of peaches. She used 30 peaches to make pies. If there were 7 peaches in each bag, how many peaches did she have left?
- Solution:
- Total peaches bought = \( 6 \times 7 = 42 \) peaches.
- Peaches used = 30.
- Peaches left = \( 42 - 30 = 12 \).
- Answer: 12 peaches

#### Problem 4.a: Circle the 18th shape in the shape pattern.
- Solution:
- The pattern repeats every 5 shapes: blue circle, lightning bolt, blue square, star, smiley face.
- To find the 18th shape, divide 18 by 5: \( 18 \div 5 = 3 \) remainder 3.
- The remainder 3 corresponds to the 3rd shape in the pattern, which is the blue square.
- Answer: Circle the blue square.

#### Problem 5.a: Decompose \( \frac{4}{7} \) and find the sum of the mixed numbers.
- Mixed numbers: \( 5 \frac{7}{9} + 1 \frac{5}{9} \)
- Solution:
- Add the whole numbers: \( 5 + 1 = 6 \).
- Add the fractions: \( \frac{7}{9} + \frac{5}{9} = \frac{12}{9} = 1 \frac{3}{9} = 1 \frac{1}{3} \).
- Combine: \( 6 + 1 \frac{1}{3} = 7 \frac{1}{3} \).
- Answer: \( 7 \frac{1}{3} \)

#### Problem 7.a: Name a line segment in the figure.
- Solution:
- A line segment is a part of a line with two endpoints.
- Example: Line segment \( AB \) or \( CD \).
- Answer: \( AB \) or \( CD \).

#### Problem 9.a: Steve bought a pair of gloves for $5.60 and a pair of socks for $2.50. If he paid with a $10 bill, how much change did he get from the cashier?
- Solution:
- Total cost = \( 5.60 + 2.50 = 8.10 \).
- Amount paid = $10.
- Change = \( 10.00 - 8.10 = 1.90 \).
- Answer: $1.90

#### Problem 10.a: Find the angle measure.
- Solution:
- The circle is divided into 8 equal parts.
- Each part represents \( \frac{360^\circ}{8} = 45^\circ \).
- Answer: 45°

---

Final Answer

The solutions for the selected problems are boxed as follows:

- Test 3:
- 1.a: \( \boxed{500,000} \)
- 2.b: \( \boxed{65,837 > 65,738} \)
- 3.a: \( \boxed{\text{10 groups of 8 is equal to 80}} \)
- 4.b: \( \boxed{48 \text{ minutes}} \)
- 5.a: \( \boxed{\frac{3}{5}} \)
- 7.a: \( \boxed{\text{Draw a right triangle}} \)
- 9.a: \( \boxed{11 \text{ feet}} \)

- Test 8:
- 1.a: \( \boxed{\text{Four hundred thirty-five thousand eighteen}} \)
- 2.a: \( \boxed{18,625 \text{ mL}} \)
- 3.a: \( \boxed{12 \text{ peaches}} \)
- 4.a: \( \boxed{\text{Circle the blue square}} \)
- 5.a: \( \boxed{7 \frac{1}{3}} \)
- 7.a: \( \boxed{AB \text{ or } CD} \)
- 9.a: \( \boxed{1.90} \)
- 10.a: \( \boxed{45^\circ} \)

Boxed Final Answer:
\[
\boxed{500,000, 65,837 > 65,738, \text{10 groups of 8 is equal to 80}, 48 \text{ minutes}, \frac{3}{5}, \text{Draw a right triangle}, 11 \text{ feet}, \text{Four hundred thirty-five thousand eighteen}, 18,625 \text{ mL}, 12 \text{ peaches}, \text{Circle the blue square}, 7 \frac{1}{3}, AB \text{ or } CD, 1.90, 45^\circ}
\]