"6th grade math syllabus" is searched by parents of a child entering middle school, where math changes from one teacher who knows the child to a period with a specialist, and by parents who have heard that the placement for accelerated math is decided this year. Both are true. This page gives the five Common Core domains in the order schools teach them, a month-by-month plan, the accelerated option and the Algebra 1 placement that starts in grade 6, the state test, the comparison with CBSE Class 6, and a twelve-question check for the end of the year. The printable checklist has every skill as a tick box.
Download the grade 6 math syllabus checklist (PDF) (the five domains with every skill as a tick box, the month-by-month plan, the accelerated track, the state test, the CBSE comparison and the twelve-question check with answers; two pages, free).
The five domains, in the order schools teach them
The Common Core State Standards for grade 6 (6.RP, 6.NS, 6.EE, 6.G, 6.SP) are used, with small changes, by most states; Texas (TEKS) and Virginia (SOL) have their own with the same content.
| Domain | What it covers | Weeks |
|---|---|---|
| 1. The number system, part 1 | Fluent multi-digit division with the standard algorithm; adding, subtracting, multiplying and dividing decimals fluently; greatest common factor (to 100) and least common multiple (to 12); the distributive property to factor a sum (36 + 8 = 4(9 + 2)); dividing a fraction by a fraction, with models and the reason the "invert and multiply" rule works | 6 |
| 2. Ratios and proportional relationships | Ratio language and notation; unit rates ("per"); tables of equivalent ratios and their graphs; solving ratio and rate problems by tables, tape diagrams and double number lines; percent as a rate per 100, finding the percent of a quantity and the whole from a part; converting units by ratio | 7 |
| 3. Expressions and equations | Whole-number exponents; writing and evaluating expressions with variables; the parts of an expression (term, coefficient, factor); equivalent expressions by the distributive property and combining like terms; solving one-step equations (x + p = q and px = q) with non-negative rationals; writing and graphing inequalities (x > c); dependent and independent variables in tables, graphs and equations | 7 |
| 4. The number system, part 2 | Negative numbers in context (temperature, elevation, debt); the number line in both directions; ordering rational numbers and reading inequalities; absolute value as distance from zero; the four quadrants of the coordinate plane; distances between points on the same horizontal or vertical line | 3 |
| 5. Geometry | Area of triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles; volume of right rectangular prisms with fractional edge lengths (V = lwh and V = Bh); polygons on the coordinate plane; nets and surface area of prisms and pyramids | 5 |
| 6. Statistics and probability | What a statistical question is; describing a distribution by its centre, spread and shape; mean, median, range, mean absolute deviation (MAD) and interquartile range (IQR); dot plots, histograms and box plots; reporting the number of observations and the units; the effect of an outlier | 4 |
Thirty-two weeks of content, which leaves time for review before the spring test. The order varies: some schools open with ratios because it motivates the fractions review; the two orderings cover the same ground by Christmas.
A month-by-month plan for the standard year
| Months | Domain | What to check at home |
|---|---|---|
| August to September | Division and decimals; GCF and LCM; dividing fractions | 7,344 ÷ 16 = 459; 3.6 × 2.5 = 9; GCF of 24 and 36 is 12; 3/4 ÷ 1/8 = 6, and can say why |
| October to November | Ratios, rates, percent | "3 : 5" read as a comparison; 240 miles in 4 hours is 60 miles per hour; 15% of 80 is 12; if 12 is 30% of a number, the number is 40 |
| December to January | Expressions and equations | 2³ = 8; 3(x + 4) = 3x + 12; x + 7 = 15 solved and checked; y = 4x as a table and a graph |
| February | Negative numbers; the coordinate plane | −8 < −3 explained with the number line; |
| March | Geometry | Area of a triangle with base 10 and height 7 is 35; volume of a 2 by 1½ by 3 box is 9; draws the net of a cube |
| April to May | Statistics; review; state test | Finds mean and median of 4, 7, 7, 9, 13; reads a box plot; says what MAD measures |
The accelerated option, and the placement that starts here
About a third of US students take Algebra 1 in 8th grade, and the decision is made in grade 6. The usual mechanism is an accelerated 6/7 course (Math 6/7, Accelerated 6, Compacted 6), which covers all of grade 6 and most of grade 7 in one year; the child then takes grade 8 math or Pre-Algebra in 7th and Algebra 1 in 8th. Placement into it is decided at the end of 5th grade or the start of 6th by a test and the teacher's recommendation; some districts test again at the end of 6th for a second entry point.
What the placement test actually checks is the three things grade 6 depends on: fractions as numbers (all four operations), multiplication facts automatic, and the habit of showing the working. A child who has those three in September will find grade 6 comfortable and the accelerated course manageable; a child without them should not be accelerated whatever the test says, because the gap reappears in Algebra 1 two years later. The whole ladder is in what grade do you take Algebra 1.
The state test
Every state tests grade 6 math in the spring. Texas's STAAR grade 6 math has 43 points, with 16 for Approaches (passing) and 25 for Meets in the latest published tables (the full table is in what grade do you need to pass the STAAR test); Florida's FAST, California's CAASPP, New York's state test and Massachusetts's MCAS cover the same domains. Ratios, rates and percent, and expressions and equations, are weighted most heavily everywhere, and they are also the two domains the Algebra 1 placement is built on, which is why a grade 6 score at Meets or above matters more than the grade 4 or 5 score did.
US grade 6 against CBSE Class 6, for families from India
| US grade 6 domain | CBSE Class 6 (NCERT) |
|---|---|
| Division and decimals; GCF and LCM | Whole Numbers; Playing with Numbers (factors, primes, HCF, LCM); Decimals: a close match, with CBSE doing more by hand |
| Dividing fractions | Fractions: CBSE Class 6 adds and subtracts; dividing fractions comes in Class 7 |
| Ratios and percent | Ratio and Proportion: a match; percent is lighter in CBSE until Class 7 |
| Expressions and equations | Algebra: a match (variables, simple equations) |
| Negative numbers | Integers: a match, but the four-quadrant coordinate plane is not in CBSE until Class 8 or 9 |
| Geometry | Basic Geometrical Ideas, Understanding Elementary Shapes, Mensuration, Symmetry, Practical Geometry: CBSE has more constructions and symmetry; the US has nets, surface area and volume with fractions |
| Statistics | Data Handling: pictographs and bar graphs in CBSE; the US adds mean, median, MAD, histograms and box plots |
A child arriving from CBSE Class 6 needs the coordinate plane, dividing fractions and the statistics vocabulary; everything else is familiar. A child leaving for India needs constructions and more arithmetic practice. The US math syllabus grade by grade has the full mapping.
A twelve-question check for the end of grade 6
Fifteen minutes, no calculator.
- 8,352 ÷ 24
- 4.8 × 3.5, and 7.2 ÷ 0.9
- The greatest common factor of 42 and 56, and the least common multiple of 6 and 8
- 5/6 ÷ 2/3
- A recipe uses 3 cups of flour for every 2 cups of sugar. How much sugar for 12 cups of flour?
- 35% of 120. And: 18 is 40% of what number?
- Write 4 × 4 × 4 with an exponent and evaluate it. Simplify 5(2x + 3) − 4x.
- Solve: x + 9 = 23, and 6y = 42. Then write the solutions of x > 4 on a number line in words.
- Order from least to greatest: −4, 3, −7, 0, 2. What is |−9|?
- Plot the point (−5, 3): which quadrant is it in? How far is it from (−5, −2)?
- A triangle has base 12 cm and height 5 cm: its area. A box is 3 by 2½ by 4 feet: its volume.
- The data 6, 9, 9, 12, 14: find the mean and the median, and say which one changes more if 14 becomes 44.
Answers: 1) 348. 2) 16.8; 8. 3) 14; 24. 4) 5/6 × 3/2 = 15/12 = 1 1/4. 5) 8 cups. 6) 42; 45. 7) 4³ = 64; 6x + 15. 8) x = 14; y = 7; all numbers to the right of 4, open circle at 4. 9) −7, −4, 0, 2, 3; 9. 10) Quadrant II; 5 units. 11) 30 cm²; 30 cubic feet. 12) Mean 10, median 9; the mean (to 16; the median stays 9).
Ten or more right: ready for grade 7 and a reasonable candidate for acceleration. Seven to nine: the missed questions name the summer work. Six or fewer, or questions 4 to 6 wrong: fractions and ratios are the gap, and they are what grade 7 and the Algebra 1 placement are built on.
Download the grade 6 math syllabus checklist (PDF)
Where to get help
A 1-on-1 online class with a tutor who holds a master's in mathematics and teaches the middle-school sequence in Common Core order: fractions made solid first, ratios with tape diagrams and double number lines the way the school draws them, equations with the balance method, and the placement-test format practised in the spring. After school or weekends, US time; the recording and notes after every class; the same tutor into grade 7 and Pre-Algebra. US$10 to $13 an hour, billed monthly. The grade 6 math page has the units; the free 30-minute class is a real lesson on this week's homework.
Questions parents ask
1What is in the 6th grade math curriculum?
2What math should a 6th grader know before the year starts?
3What is accelerated 6th grade math?
4Is there a state test in 6th grade?
5How does US grade 6 compare with CBSE Class 6?
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