Hawaii SBAC Grade 6 Math Free Worksheets: Printable Practice Worksheets with Worked Solutions

Sixth-grade math is a bridge year. On one side is the arithmetic of the elementary grades — adding, subtracting, multiplying, dividing whole numbers and fractions. On the other side is the algebra and reasoning of middle school. Sixth grade is the span itself, the part where a student has to keep their footing while the ground changes from “find the answer” to “explain the relationship.” Plenty of capable kids wobble on that bridge, and it is not because they got worse at math — it is because math got different.

The year asks for a lot. Ratios, rates, and percents become a way of seeing. Multi-digit and decimal operations need to be not just correct but fluent. The number line runs below zero, and the coordinate plane opens into four quadrants. Letters arrive in expressions, and one-step equations and inequalities arrive with them. There is area, volume, and surface area, with nets folding flat shapes into solids. And there is a first real run at statistics — mean, median, spread, dot plots, box plots — plus an opening look at probability. From Honolulu to Hilo, from Kailua to Pearl City, that is the work in front of every sixth grader.

These worksheets were built to make the crossing one steady plank at a time.

What’s on this page

Seventy-two single-skill PDFs, each aligned to the Hawaii Mathematics Standards at Grade 6. Every file carries one skill and only that skill — so a student working on percent of a number is not also untangling surface area, and a student practicing one-step equations is not sidetracked into box plots.

Each PDF begins with a one-page Quick Review that explains the skill in plain language and works one example all the way through. Then twenty practice problems build from gentle to genuinely challenging, and four word problems put the skill into a real situation. The final page is a student-facing answer key, written so a sixth grader can read it alone — short, friendly explanations that turn checking the work into part of the lesson.

Ratios, Rates, and Percents

• What Is a Ratio? — [6.RP.1] compare two quantities and write the comparison three ways
• Using Ratio Language — [6.RP.1] describe a ratio in words — ‘for every,’ ‘to,’ and ‘per’
• What Is a Rate? — [6.RP.2] a ratio that compares two different units, like miles per hour
• Finding the Unit Rate — [6.RP.2] divide to find the cost or amount for exactly one
• Tables of Equivalent Ratios — [6.RP.3] build a ratio table and fill in the missing values
• Graphing Ratios — [6.RP.3] plot a ratio table and see the straight line it makes
• What Is a Percent? — [6.RP.3] a percent is just a ratio out of 100 — and how to read it
• Solving Percent Problems — [6.RP.3] find the part, the percent, or the whole
• Solving Rate and Ratio Word Problems — [6.RP.3] turn a real-world story into a ratio you can solve
• Converting Measurement Units — [6.RP.3] use ratios to switch between units like feet and inches
• Personal Financial Literacy — [6.RP.3] real-money math: prices, tips, and simple percent work
• Proportional vs. Non-Proportional Relationships — [6.RP.2] tell which relationships keep a constant ratio and which don’t
• Financial Literacy: Budgeting and Saving — [6.RP.3] plan a budget, track spending, and set a savings goal
• Ratios with Scale Drawings — [6.RP.3] use a scale to move between a drawing and real life

The Number System

• Dividing Fractions by Fractions — [6.NS.1] multiply by the reciprocal — and understand why it works
• Multi-Digit Division — [6.NS.2] the standard algorithm for dividing large whole numbers
• Decimal Operations — [6.NS.3] add, subtract, multiply, and divide decimals cleanly
• Greatest Common Factor and Least Common Multiple — [6.NS.4] find the GCF and LCM and know when to use each
• The Distributive Property with Common Factors — [6.NS.4] rewrite a sum by pulling out the greatest common factor
• Understanding Positive and Negative Numbers — [6.NS.5] what negative numbers mean in temperature, money, and elevation
• Opposites and Absolute Value — [6.NS.7] opposites flip the sign; absolute value is distance from zero
• Rational Numbers on the Number Line — [6.NS.6] place fractions, decimals, and negatives exactly where they go
• The Coordinate Plane — [6.NS.6] plot points in all four quadrants using ordered pairs
• Comparing and Ordering Rational Numbers — [6.NS.7] use the number line to order positives, negatives, and fractions
• Distance on the Coordinate Plane — [6.NS.8] find the distance between two points that share a line
• Integer Addition and Subtraction — [6.NS.5] add and subtract positives and negatives with confidence
• Integer Multiplication and Division — [6.NS.5] the sign rules for multiplying and dividing integers
• Compute with Integers in Context — [6.NS.5] real situations where negative numbers do the work

Expressions and Equations

• Exponents and Order of Operations — [6.EE.1] evaluate powers and run PEMDAS in the right order
• Translating Words into Expressions — [6.EE.2] turn a phrase into an algebraic expression
• Terms, Factors, and Coefficients — [6.EE.2] name the parts of an expression so you can talk about them
• Evaluating Expressions — [6.EE.2] substitute a value for the variable and compute
• Equivalent Expressions — [6.EE.3] use properties to show two expressions are the same
• Variables in Real-World Problems — [6.EE.6] let a letter stand for an unknown and model a situation
• Solving One-Step Equations — [6.EE.7] undo one operation to isolate the variable
• Writing Inequalities — [6.EE.8] translate ‘at least,’ ‘no more than,’ and ‘fewer than’ into symbols
• Graphing Inequalities on a Number Line — [6.EE.8] open or closed circle, then shade the right direction
• Two Quantities That Change Together — [6.EE.9] independent and dependent variables, tables, and graphs

Geometry

• Area of Triangles — [6.G.1] one-half base times height — for every kind of triangle
• Area of Parallelograms and Trapezoids — [6.G.1] the area formulas for two more four-sided shapes
• Volume of Rectangular Prisms — [6.G.2] volume with fractional edge lengths, using unit cubes
• Polygons on the Coordinate Plane — [6.G.3] draw a polygon from coordinates and find its side lengths
• Finding Area on the Coordinate Plane — [6.G.3] use coordinates to find the area of a plotted figure
• Nets and Surface Area — [6.G.4] unfold a solid into a net and add up every face
• Transformations on the Coordinate Plane — [6.G.3] slide and reflect figures and track the new coordinates
• Area of Circles Introduction — [6.G.1] a first look at radius, diameter, and the area of a circle

Statistics and Probability

• Statistical Questions — [6.SP.1] tell a question that has variability from one that does not
• Describing Data: Center, Spread, and Shape — [6.SP.2] the three things every data set has — and how to name them
• Mean and Median — [6.SP.3] two measures of center and when each one tells the truth
• Measures of Spread — [6.SP.3] range and mean absolute deviation — how spread out the data is
• Dot Plots and Histograms — [6.SP.4] two ways to picture how often each value shows up
• Box Plots — [6.SP.4] the five-number summary and the box it builds
• Summarizing Data and Making Comparisons — [6.SP.5] describe a data set in a sentence and compare two of them
• Introduction to Probability — [6.SP.5] how likely is it — from impossible to certain, as a number
• Stem-and-Leaf Plots — [6.SP.4] organize a data set while keeping every original value
• Circle Graphs — [6.SP.4] read a pie chart and connect each slice to a percent
• Data Displays Extended — [6.SP.4] choose the right graph and read it carefully

Number and Operations Practice

• Writing Ratios in Different Forms — [6.RP.1] the same ratio as a fraction, with a colon, and in words
• Equivalent Ratios — [6.RP.3] scale a ratio up or down and keep it the same
• Comparing Unit Rates — [6.RP.2] find the better buy by comparing rates for one
• Proportions and Cross Multiplication — [6.RP.3] set two ratios equal and solve for the missing value
• Simplifying Fractions — [6.NS.4] divide out the common factor to write a fraction lowest-terms
• Adding Fractions with Unlike Denominators — [6.NS.4] find a common denominator, then add
• Subtracting Fractions with Unlike Denominators — [6.NS.4] find a common denominator, then subtract
• Adding and Subtracting Mixed Numbers — [6.NS.4] work with the whole and fraction parts, including regrouping
• Multiplying Fractions — [6.NS.1] multiply across — and simplify before or after
• Multiplying Mixed Numbers — [6.NS.1] rename as improper fractions, then multiply
• Dividing Fractions — [6.NS.1] keep, change, flip — divide by multiplying the reciprocal
• Dividing Mixed Numbers — [6.NS.1] rename as improper fractions, then divide
• Decimal Place Value — [6.NS.3] name each digit’s value, from tenths to thousandths
• Comparing and Ordering Decimals — [6.NS.7] line up the place values and order decimals correctly
• Area of Rectangles and Squares — [6.G.1] length times width — including fractional and decimal sides

How to use these worksheets at home

The simplest plan is the one you can actually keep. Two short sittings a week, one PDF each, fifteen to twenty minutes — that beats a long, dreaded study session every time, because a sixth grader will show up for something small and finishable.

The real leverage is in pairing. These files stand alone, but skills travel in families, and a family worked together gets easier with each sheet. Pair “What Is a Ratio?” with “Finding the Unit Rate.” Pair “Dividing Fractions by Fractions” with “Dividing Mixed Numbers.” Pair “Plotting Points on the Coordinate Plane” with the worksheets that reach into the negative quadrants. When the second sheet rests on the first, a student feels the ground holding instead of shifting.

Island life has its own rhythms — the drive home along the coast, the afternoon before the water cools, the slow part of the evening after dinner. Tuck the worksheet into one of those rhythms rather than carving out something new. Print the PDF the night before so it is ready and waiting, keep the answer key back until the work is finished, then hand it over and let your child grade their own page. Reading the explanation for a missed problem is quiet work, and it is where the understanding actually takes hold.

A note about SBAC at Grade 6

Hawaii sixth graders take the Smarter Balanced (SBAC) Mathematics assessment in the spring. It is built on the Hawaii Mathematics Standards, which are aligned to the Common Core, so the skills on these worksheets and the skills on the test come from the same source.

At Grade 6, the SBAC asks for more than a number. It is a computer-based test that expects students to reason about ratios and rates, set up and solve a one-step equation from a word problem, interpret a data display, and choose an approach that fits the question — sometimes in multi-step items that ask them to show their thinking. Because every PDF here targets a single standard, the spring window becomes a checklist: you can see exactly where your child is solid and where they need another pass, and put your time only where it matters.

A short closing

Sixth-grade math is a bridge, and a student crosses it one plank at a time, not in a single leap. Bookmark this page, print a single PDF tonight, and let your child start somewhere small and steady. Hawaii kids handle hard things well when the next step is clear — and a worksheet on the table is about as clear as a next step gets.

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