Caveat Academy · Math · Grades 3 to 8

Find the gaps.
Fill them in order.

A twenty-minute placement check across grades 3 to 8 math finds the skills that are solid and the ones to build. Then a personal plan: the right lessons from the full-year math courses, in order, with a short mastery check each week and a plain summary for parents.

Buy now, $24How the placement works
36skills placed
7strands
63lessons it can point to
20minutes to place

How it works

For a student who is stuck on old skills, more of this year's work does not help much. Finding the exact skills and fixing them in order does.

  1. The placement check, about 20 minutes. The student picks the grade they are in. Questions start near that grade and adapt: a miss steps down to an earlier skill, a hit steps up. Each step asks two questions, and a third if they split, so one slip does not move the student.
  2. The personal sequence. Every skill to build becomes a step in an ordered checklist, earliest skills first. Each step links straight to the lesson for it in the Caveat Academy full-year math courses, and to a Protégé topic where one fits.
  3. The weekly mastery check. Four short questions per skill. Three right and the skill is mastered. If not, back to the lesson and try again the next day or later, with a different set of questions.
  4. The parent summary. Skills that are strong, skills to build, what showed up in the answers and this week's plan, in plain words. It never labels a child by grade level.

What the answers can show

Many wrong answers are not random. They come from a wrong idea that makes sense to the student. The placement listens for them and says which ones showed up:

  • Adds the tops and the bottomsAdds fractions by adding the numerators and adding the denominators, so 1/2 + 1/3 comes out as 2/5. The pieces have to be the same size before they can be added.
  • Bigger bottom number, bigger fractionReads a larger denominator as a larger fraction, so 1/8 looks bigger than 1/5. Cutting the same whole into more pieces makes each piece smaller.
  • Longer decimal, bigger numberTreats a decimal with more digits as larger, so 0.375 looks bigger than 0.4. Comparing place by place, starting with tenths, fixes it.
  • Negative signs get lostDrops or flips a negative sign when adding, subtracting, multiplying or dividing. A number line and the sign rules, said out loud, help.
  • Multiplies only the first termMultiplies only the first term inside parentheses, so 3(x + 4) becomes 3x + 4. The number outside multiplies every term inside.

43 wrong ideas in all, each with the skill and lesson that repair it. Where a Protégé topic fits, the plan links it: the student teaches Pip, a classmate who holds that same wrong idea, until Pip gets it right.

Seven strands, grades 3 to 8

36 skills follow the usual order of the math standards from grade 3 to grade 8. The placement only asks about strands that make sense for the student's grade.

Number sense and place value

  • Place value and rounding to 1,000
  • Place value to a million; comparing and rounding
  • Powers of 10 and place value
  • Negative numbers and absolute value
  • Fractions as decimals
  • Square roots and irrational numbers

Operations and fluency

  • Multiplication and division facts
  • Multi-digit multiplication and division with remainders
  • Multiplying multi-digit numbers and dividing by two-digit numbers
  • Order of operations and exponents
  • Adding, subtracting, multiplying and dividing negative numbers
  • Exponent rules and scientific notation

Fractions

  • Unit fractions, the number line and comparing
  • Equivalent fractions; adding like fractions
  • Adding and subtracting fractions with unlike denominators
  • Multiplying fractions
  • Dividing fractions

Decimals and percents

  • Tenths and hundredths
  • Comparing, rounding, adding and subtracting decimals
  • Multiplying and dividing decimals
  • Percents of a number
  • Percent increase, decrease, discounts and tips

Ratios and proportions

  • Ratios, ratio tables and unit rates
  • Proportional relationships and scale
  • Slope as a rate of change

Expressions and equations

  • What the equals sign means; unknown numbers
  • Writing and evaluating expressions
  • The distributive property and equivalent expressions
  • Two-step equations and simplifying expressions
  • Multi-step equations

Geometry and measurement

  • Area and perimeter of rectangles
  • Measurement units and conversions
  • Volume of rectangular prisms
  • Area of triangles and parallelograms; surface area
  • Circumference and area of circles
  • The Pythagorean theorem

The placement check

  • Original questions, written for this check: number sense, operations, fractions, decimals and percents, ratios, expressions and equations, and geometry and measurement.
  • Typed answers for most questions; equivalent forms count, so 1/2, 2/4 and 0.5 are all right for one half. Some questions are multiple choice.
  • An "I have not learned this yet" button on every question. No timer and no score on screen.
  • Stop any time and pick up later on the same device.

A question from the check

FractionsWhat is 1/2 + 1/3?

If a student types 2/5, the plan notes the wrong idea behind it:

  1. Adds the tops and the bottoms.
  2. The step for adding fractions with unlike denominators links the lessons that fix it.

The weekly mastery check

The plan sets one, two or three skills a week. When the lessons are done, the student takes the check: four questions per skill, with the answer shown after each one. Three of four is mastered.

If a skill does not stick, the step stays in the plan, the lesson comes first, and the next check opens the following day with a different set of questions. After two tries, the plan suggests teaching it to Pip, asking the Caveat Tutor for hints inside the lesson, or asking a teacher.

The parent summary

One page, printable, in plain words:

  • Skills that are strong, by strand.
  • Skills to build, in the order the plan takes them, and which are mastered.
  • What showed up in the answers, and what each wrong idea means.
  • This week's lessons and check, and how to help at home.

It reports skills. It never says a child is behind by some number of grades, and it is not a test score or a diagnosis.

Math Foundations with Placement

The placement check, the personal plan and the weekly mastery checks for one student, built for a semester of steady work. Retake the placement at the end to see what moved.

$24one student, a semesterBuy now

Buy now adds it to your cart; check out with a card. Included with Caveat family access and with school licenses that include courses: the button opens it.

For schools

Schools get Math Foundations for every student through a Caveat school license that includes courses, along with the full-year math courses the plans link to. See school licenses.

Privacy

The placement, the plan and the checks are saved only in the browser on the device the student uses. Nothing about the student is sent to Caveat or anyone else, and one button deletes it all.

Math Foundations is practice and placement for skills, not an evaluation. It does not diagnose dyscalculia or any learning disability. If math stays hard after steady practice, the Caveat Lens Learning Skills Check and a conversation with the school are the next steps.

The other branches

One brand. Seven branches. Every grade, every next step.

For teachersCaveat Classroom

Resources made to order, free tools, professional development, certification prep.

For parentsCaveat Co-Op

Homeschool from kindergarten to grade 12, courses for parents, and plans with your Caveat advisor.

For college-bound students and familiesCaveat College

College credit in high school, the college list, applications, paying for college and the move to college.

For families with questions about learningCaveat Lens

Screeners for grades 1 to 8 that help you decide whether to ask for a full evaluation.

For social-emotional learningCaveat Cares

Feelings, friendships and self-regulation, for students, families and teachers.

For career exploration and readinessCaveat Careers

A free Career Explorer, career pathways and electives, and getting ready for a first job.

The Caveat Family Guide to College is general information, not legal, tax or financial advice. Each college decides admission, aid and how credit counts, and requirements change; check each college's own pages. Examples are examples, not promises. Caveat Academic Services is an independent college preparation company. Students do all of their own work.