Sixth Grade Daily Math Curriculum Workbook - Free Printable

Here are the solutions for the homework problems shown in the worksheet.

WEDNESDAY: Geometry

1. Classify the angle.
* Reasoning: The image shows a straight line with an arc indicating the angle covers the entire straight path. A straight line represents an angle of 180 degrees.
* Answer: Straight angle

2. Is this an equilateral triangle?
* Reasoning: An equilateral triangle must have three sides of equal length and three angles of equal measure (60°). The triangle shown has sides of clearly different lengths and appears to have a right angle (90°). Therefore, it is not equilateral.
* Answer: No

3. Which 3D figure has no faces?
* Reasoning:
* A triangular prism has 5 flat faces.
* A cone has 1 flat face (the base) and 1 curved surface.
* A cylinder has 2 flat faces (top and bottom) and 1 curved surface.
* A sphere is perfectly round and has only a curved surface; it has zero flat faces.
* Answer: B. sphere

4. Calculate the measure of the missing angle.
* Reasoning: The sum of all angles inside any triangle is always 180°.
* Given angles: $140^\circ$ and $20^\circ$.
* Add them together: $140 + 20 = 160$.
* Subtract from the total: $180 - 160 = 20$.
* Answer: $20^\circ$

5. Are these shapes congruent or similar?
* Reasoning:
* Congruent means shapes are exactly the same size and shape.
* Similar means shapes have the same shape but can be different sizes.
* Looking at the two triangles, they appear to be identical in size and side lengths, just rotated slightly. Because they are the exact same size, they fit the definition of congruent. (Note: All congruent shapes are also technically similar, but "congruent" is the more precise answer for identical shapes).
* Answer: Congruent

---

THURSDAY: Measurement

1. How are the area of a parallelogram and the area of a rectangle related?
* Reasoning: If you cut off the triangular corner of a parallelogram and move it to the other side, it turns into a rectangle. They both use the same formula: $\text{Base} \times \text{Height}$ (or $\text{Length} \times \text{Width}$).
* Answer: They use the same formula ($\text{Base} \times \text{Height}$). You can turn a parallelogram into a rectangle by moving a piece from one side to the other.

2. $5.6 \text{ m} = \_\_\_\_ \text{ dm}$
* Reasoning: There are 10 decimeters (dm) in 1 meter (m). To convert meters to decimeters, multiply by 10.
* $5.6 \times 10 = 56$.
* Answer: $56$

3. $3 \text{ years} = \_\_\_\_ \text{ weeks?}$
* Reasoning: There are 52 weeks in 1 year.
* $3 \times 52 = 156$.
* Answer: $156$

4. Chris got home from baseball practice at 5:30 pm. What time is that in 24 hour notation?
* Reasoning: To convert PM times to 24-hour notation, add 12 to the hour.
* $5 + 12 = 17$.
* Keep the minutes the same (:30).
* Answer: 17:30

5. What is the area? Round to the nearest hundredth. Assume $\pi = 3.14$.
* Reasoning:
* The image shows the radius ($m$) is 16.
* Formula for Area of a Circle: $A = \pi \times r^2$.
* Step 1: Square the radius. $16 \times 16 = 256$.
* Step 2: Multiply by $\pi$ ($3.14$).
* Calculation: $256 \times 3.14 = 803.84$.
* Answer: $803.84$