Grade 6–7 Math: Integers, the Coordinate Plane, Circles, Area and Volume Units
Grade 6–7 Math: Integers, the Coordinate Plane, Circles, Area and Volume
A Grade 6 student can say that -7 is less than -3 and still plot (-4, 5) in the wrong quadrant. A Grade 7 student can recite the formula for circle area and then use it for circumference. Both are common. The two units here ask students to explain which quantity they found and why, not only to give a number.
See the Grade 6 unit →Resources that fit
Math units for Grades 6–7 and what sits beside them
The Grade 6 and Grade 7 math units are the core. The map skills unit reuses coordinates and scale, and the engineering unit offers a hands-on change of pace.
Integers and the Coordinate Plane | 8 Lessons, 8 Challenges & a Project | Grade 6
Signed quantities, absolute value, four quadrants and reflections as sign changes.
Circles, Area and Volume | 8 Lessons, 8 Investigations & a Project | Grade 7
Circumference, circle area, composite regions, prism volume and surface area.
Map Skills and GIS Basics | 8 Lessons, 8 Case Cards & a Fictional GIS Dataset | Grades 6–7
Coordinates and scale taught through maps and a fictional GIS dataset.
Engineering Design Challenges | 8 Challenges, Case Cards & a Project | Grades 6–8
Eight paper-based design challenges where students justify their decisions.
Multiplication Fact Fluency | Strategies, Fact Families & Array Labs | Grade 3
Earlier fact fluency for students who still count on for multiplication.
Lesson sequence
The two units, lesson by lesson
| Lesson | Integers and the Coordinate Plane (Grade 6) | Circles, Area and Volume (Grade 7) |
|---|---|---|
| 1 | Signed quantities | Radius and diameter |
| 2 | Order | Circumference |
| 3 | Opposites | Circle area |
| 4 | Absolute value | Semicircles |
| 5 | Four quadrants | Composite regions |
| 6 | Coordinate distance | Prism volume |
| 7 | Reflections as sign changes | Surface area |
| 8 | A coordinate game | Measurement decisions |
Both units add eight extra tasks (coordinate challenges in Grade 6, geometry investigations in Grade 7), a precise model and interpretation page, two vocabulary pages, a learning check and a short project with a reflection page. You can start with Integers and the Coordinate Plane in Grade 6 and move to Circles, Area and Volume the following year.
Grade 6
Integers, absolute value and the plane
The Grade 6 unit starts on the number line. Lessons 1 to 4 cover signed quantities, order, opposites and absolute value, so students first read positive and negative numbers in everyday situations before they compare them. From lesson 5 the work moves into the four quadrants, then distance between points and reflections described as sign changes. The closest standard is CCSS 6.NS.C, which covers rational numbers, absolute value and the coordinate plane. No alignment is claimed. Each lesson ends in a case card where the student chooses an approach and justifies it. That is useful for absolute value, because students often confuse it with simply dropping a sign. The teacher guide has 21 pages with answers, keys for the eight coordinate challenges and an assessment key with feedback.
Grade 7
Circles, area and volume
The Grade 7 unit begins with radius and diameter, then separates circumference from circle area, a mix-up that shows up every year. Semicircles and composite regions follow, and students split combined shapes into pieces they already know. The last lessons build prism volume from the area of the base, then surface area, and end with a lesson on choosing the right measure and defending the choice. The closest standards are CCSS 7.G.B.4 (circumference and area of a circle) and 7.G.B.6 (area, volume and surface area). Again, no alignment or endorsement is claimed. The case cards ask students to interpret a result in context, so a correct calculation with the wrong unit or the wrong measure does not pass unnoticed.
UK and Australia
Years 7–8 in the UK and Australia
Year groups do not line up exactly with US grades, so check the topics against your own scheme of work. Integers, the four-quadrant coordinate plane, circles, area and volume all appear in the Key Stage 3 range, which covers Years 7 to 9 in England, and in Years 7 and 8 in Australia. Teachers in those systems can use either unit as a self-contained block and skip lessons they have already covered, since the lessons can be used in order or picked individually. The text follows US conventions, so expect grade labels and CCSS names in places. For worksheets organised by Key Stage, see UK KS3 maths worksheets. The units themselves make no claim of fit to any national curriculum.
Beside the core units
Coordinates in geography, design tasks and earlier gaps
Coordinates and scale come up again in Map Skills and GIS Basics, a Grades 6–7 unit that asks students to find positions with a coordinate system and work with map scale. It is a geography unit, so use it as a second context, not as extra math practice. For a break from worksheets, Engineering Design Challenges has eight paper-based tasks in which students justify their design decisions in writing. Some students arrive in Grade 6 with shaky multiplication facts. Multiplication Fact Fluency is a Grade 3 unit that can serve as a reference point for that gap. For the step after both units, see middle school pre-algebra worksheets.
In practice
Sequencing the two units
- Check the prerequisitesAsk students to order integers and name a point on a grid. Gaps in multiplication facts show up early.
- Start with the number lineIn Grade 6, teach lessons 1 to 4 before the plane. Absolute value needs the number line first.
- Use the case cardsCollect the case card after each lesson. The written reason shows which quantity the student found.
- Separate the measuresIn Grade 7, keep circumference, area and surface area apart with the practice pages before mixing them.
- Finish with the checkUse the learning check, project and reflection page to close each unit.
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Questions teachers ask
Frequently asked questions
Which standards do the math units fit?
Integers and the Coordinate Plane is closest to CCSS 6.NS.C. Circles, Area and Volume is closest to CCSS 7.G.B.4 and 7.G.B.6. No alignment or endorsement is claimed.
Are answers included?
Yes. Each unit has a separate 21-page teacher guide with answers and teaching notes for all eight lessons, keys for the eight challenges or investigations and an assessment key with feedback.
How long does each unit take?
The material does not state a duration. Plan by lesson: each has three pages, and you can use the lessons in order or pick the ones you need.
Can I use the Grade 7 unit with a strong Grade 6 class?
The unit is written for Grade 7, so read the lessons first. Lessons can be used individually, which lets you choose the ones that suit the class.
Is this suitable for Years 7–8 in the UK or Australia?
The topics sit in that age range, but the units make no claim of fit to any national curriculum. Compare the lesson list in the table with your scheme of work.
Can I edit the pages?
Yes. Each unit includes editable DOCX text editions of the classroom material and the teacher guide. The PDF is the print reference, and DOCX line breaks may differ.
Ask students to explain the number
Two eight-lesson math units for Grades 6 and 7, with answers in the teacher guide.
See the Grade 6 unit →