Grade 6 | MATHEMATICS
STUDENT WORKBOOK • Unit 1
Mathematics only. No Language Arts, Science, History or Scripture assignments appear in this workbook.
MATHEMATICS STUDENT PDF: Download or fill in this grade’s Mathematics-only workbook. The Math lesson and problems on this page remain copyable and printable. Save completed PDF answers privately in your own PDF app. This is Unit 1, not the full annual Math textbook.
Lesson 1: Ratios, rates and signed numbers
Learn the Concept
Teacher explanation: A ratio compares quantities. A unit rate gives a comparison per one unit. If 12 miles are traveled in 3 hours, the average rate is 4 miles per hour. Signed numbers locate quantities above and below zero.
Guided Example
Read the example in the lesson explanation. Use a drawing, number line, manipulatives or written equation to explain each step to a parent or teacher.
Independent Practice: 10 Problems
- Simplify ratio 18:30.
- Solve 3/5=x/40.
- Find rate for 150 miles in 3 hours.
- Order -4,-9,0,3.
- Compute -7+12.
- Compute -5-8.
- Compute 2/3 divided by 1/6.
- Evaluate 4x+7 when x=5.
- Find area of a triangle with base 12 and height 5.
- Advanced: write and solve a two-step real-world unit-rate problem with proper units.
Check Your Work
Show the steps for at least two problems and explain how you know your answer is reasonable. If you find an error, correct it and try a different example.
Advanced Scholar Extension
When these problems are easy, use the next grade’s mathematics unit or the Advanced Scholars pathway after showing mastery. Do not accelerate solely because of age.
Printable Work and Parent Help
Print or save: The Mathematics questions above can be copied or printed. For an independent, Mathematics-only fillable student workbook, use the PDF download link at the top of this page. The combined edition is archived separately and is not part of this Mathematics book.
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Mathematics: Type Answers Here
Complete this Mathematics-only worksheet online, then print before leaving. Website fields do not submit or save your answers. For dependable saving, use the fillable Mathematics student PDF in a compatible PDF viewer.
Grade 6 Mathematics | Five-Day Core Extension
This five-day extension strengthens the published Unit 1 with direct instruction, original practice and an independent check. It is not the complete annual Grade-level Mathematics textbook.
Day 1: Ratios and Rates
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A ratio compares two quantities. 18:30 simplifies by dividing both terms by six to 3:5. Unit rate divides a quantity by its number of units: 150 miles in 3 hours means 50 miles per hour.
- 1. Simplify 12:20
- 2. 240 miles in 4 hours
- 3. 3 notebooks cost $12. Cost per notebook?
- 4. Find x in 3/5 = x/40
Show equations or diagrams used and explain the reasoning. The fifth-day check is independent.
Day 2: Integers and Number Lines
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Negative numbers lie left of zero. Addition can be modeled as movement: -7 + 12 = 5. Subtracting a positive number moves left: -5 – 8 = -13.
- 1. Order -4, -9, 0, 3 ascending
- 2. -7 + 12
- 3. -5 – 8
- 4. -3 + -6
Show equations or diagrams used and explain the reasoning. The fifth-day check is independent.
Day 3: Fraction Division
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Dividing by a fraction asks how many fractional groups fit. 2/3 ÷ 1/6 = 4 because four sixths make two thirds. Multiplying by the reciprocal provides the general rule.
- 1. 3/4 ÷ 1/8
- 2. 2/3 ÷ 1/6
- 3. 5/6 ÷ 5/12
- 4. 3 ÷ 1/2
Show equations or diagrams used and explain the reasoning. The fifth-day check is independent.
Day 4: Expressions and Area
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Evaluate an expression by substituting a value. If x=5, 4x+7=27. The area of a triangle is one half of its base times its perpendicular height.
- 1. 4x+7 for x=5
- 2. 2a-3 for a=9
- 3. Triangle base 12, height 5
- 4. Triangle base 9, height 8
Show equations or diagrams used and explain the reasoning. The fifth-day check is independent.
Day 5: Independent Check
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Use ratio reasoning, signed operations, fractions and algebra.
- 1. Simplify 21:35
- 2. -12 + 19
- 3. 3/5 ÷ 1/10
- 4. 5x-4 for x=7
Show equations or diagrams used and explain the reasoning. The fifth-day check is independent.
Spiral Review
Begin each new lesson by recalling two previous skills with different numbers. After the independent check, design a new problem involving a skill from this unit and solve it with a clear explanation.