Middle School Math Placement Tests

From Our House to Yours

Need help with math placement for your middle school students?  Well, this blog is here to help!

Middle school students vary greatly in math skills and abilities. Heart of Dakota understands age is only one piece of the math placement puzzle. This is why every Heart of Dakota guide includes multiple math levels of instruction. One child might be advanced in math, one more average, and one struggling. Heart of Dakota has plans for all types of math students. Proper math placement is important. By matching children to their current math skills, all children can move forward and improve. If math placement is off, children and parents alike are frustrated. It is impossible to move forward in math skills if you start with a math placement that is too hard or to easy. So, how can you choose the proper math placement for your middle school student? Well, that’s what this blog post is all about!

A Brief Explanation of the Middle School Curriculum Principle of Mathematics

Principles of Mathematics is a Christian curriculum aimed at grades six through eight. It is best to use Principles of Mathematics one or two years prior to starting high school algebra. If following traditional grade levels, Principles of Mathematics Book 1 would be completed in grade six or seven, and Principles of Mathematics Book 2 would be completed in grade seven or eight. Book 1 covers the core principles of arithmetic and geometry (along with some statistics), while Book 2 builds on those principles as it introduces the core principles of algebra, probability, and trigonometry (along with more statistics).

The curriculum consists of the Student Textbook and the Teacher Guide. The Student Textbook contains the lessons, and the Teacher Guide contains all the worksheets, quizzes, and tests, along with an Answer Key and suggested schedule. Each lesson takes about 30-45 minutes, with a pace of 4-5 days a week.

A Brief Overview of the Principles of Mathematics Book 1: Placement Test

Principles of Mathematics designed this test to help determine if a middle school student is ready to begin Book 1 of Principles of Mathematics. If students get problems wrong on the placement test, check to see if they made a careless error or if they truly didn’t understand a concept. It’s okay if students make a few errors; however, it’s important that students are familiar with these concepts before beginning Book 1:

  • addition
  • subtraction
  • multiplication
  • division
  • decimals (including adding, subtracting, multiplying, and dividing them)
  • fractions (including adding, subtracting, multiplying, and dividing them)

Middle school students also need to have the mental development to explore problem solving, which will be emphasized in Book 1. Note: Book 1 will review addition, subtraction, multiplication, division, decimals, and fractions, so if middle school students struggle with any of those concepts they will get practice and reinforcement; however, it should not be the first time they’re encountering them.

A Brief Overview of the Principles of Mathematics Book 2: Placement Test

Principles of Mathematics designed this test to help determine if a middle school student is ready to begin Book 2 of Principles of Mathematics or if they need to start in Book 1. You may explain the instructions and terms on the test as needed. The point is to see if students have the skills to solve the problems. If students get problems wrong on the placement test, check to see if they made a careless error, didn’t understand the instructions, or if they truly didn’t understand a concept. It’s okay if students make a few errors, but it’s important that middle school students understand these concepts before beginning Book 2, as they are only very briefly reviewed in Book 2:

  • basic math skills (including rounding and working with decimals)
  • fractions
  • unit conversion
  • negative numbers
  • geometry formulas (finding perimeter, area, and volume)
  • exponents
  • problem-solving skills

If you feel your middle school student could use a deeper understanding of arithmetic (place value, basic operations, decimals, fractions, etc.), the basics of geometry, or problem-solving skills, we recommend starting with Book 1 even if your student can pass this placement test. Book 1 stresses those concepts, while Book 2 focuses more on pre-algebra concepts.

Clickable Links for the Principles of Mathematics Placement Tests and for Samples of the Teacher Guides and Student Books 

Need the Book 1 placement test? Click here!

For the Book 2 placement test, click here!

To check out samples of the Book 1 Teacher Guide, click here.

Or, to check out samples of the Book 1 Student Book, click here.

For the Book 2 Teacher Guide samples, click here.

Or, for the Book 2 Student Book samples, click here.

How to Order What You Need After Scoring Your Middle School Students’ Placement Test(s)

Once you have scored your student’s math placement test(s), if you know what level to start with, simply order from Heart of Dakota the appropriate Teacher’s Guide and Student’s Book. You can order those here by clicking and scrolling to the math sections: Principles of Mathematics Teacher’s Guide Book 1 and Student Book 1, or Principles of Mathematics Teacher’s Guide Book 2 and Student Book 2. If you have scored your children’s math placement tests, and are still confused about which level to start with, simply give Heart of Dakota a call or an email. Explain what you learned from the math placement tests, how they went overall, and what scores your children made on the math placement tests you gave. We can figure it out together!

Still not sure? Well, here are some pretty standard sequence options for middle school students who have or have not been using Singapore Primary Mathematics.

If you have a middle school student who has been using Singapore’s Primary Mathematics, that student has several math paths. An average math student doing well with Singapore Primary Mathematics could use 5A/5B for sixth grade, 6A/6B for seventh grade, and Principles of Mathematics Book 2 for eighth grade. A struggling math student who is not doing as well with Singapore Primary Mathematics could use 5A/5B for sixth grade, Principles of Mathematics Book 1 for seventh grade, and Principles of Mathematics Book 2 for eighth grade. An advanced math student doing well with Singapore Primary Mathematics could use 6A/6B for sixth grade, Principles of Mathematics Book 2 for seventh grade, and do Algebra 1 for eighth grade.

If you have a middle school student who has not been using Singapore Primary Mathematics, Principles of Mathematics is also an excellent option!

What if your middle school students scored lower on the math placement tests?

If your middle school students scored lower on their math placement tests, do not be dismayed! We take children where they are in math and steadily move them forward. To move children more quickly through math levels, never double up math lessons in one day. Rather, do one math lesson each day, but do math more days. One easy way to do this is to do five days of math lessons even when using four-day-a-week Heart of Dakota guides. Or, do one extra math lesson on Saturdays.  Or, do three or four extra math lessons three or four days a week during a summer break. Little by little, students will catch up!

In Christ,
Julie

A Smooth Transition from Singapore Primary Math to High School Algebra

Dear Carrie, 

We have used Heart of Dakota from the very beginning and loved it! My son will be in Missions to Modern Marvels this year. He has now completed all of the Singapore Primary Mathematics books through 6A/6B, which he finished in Revival to Revolution. I am a bit confused by all the different math options this year. I’m guessing we will transition to Videotext or No-Nonsense Algebra?  Foerster’s Algebra seems too much for an 8th grader! Is there a math choice that is the natural progression after finishing all the Singapore math books? I maybe should add that he is good at math and is even looking forward to more algebra! I don’t want to push him too hard, but he also will be discouraged if he’s not being challenged. So, what math would be the best bridge to get him from Singapore 6B to algebra in World Geography?

Sincerely,

“Ms. Confused about Math”

Dear “Ms. Confused about Math,”

There are a lot of terrific things about the Singapore Primary Mathematics U.S. Edition 1A through 6B! However, one difficulty is that it stops after 6B and switches to a new writer and a new format! As high school approaches, it can be tough to figure out a good transition between one math program and another. Since one size doesn’t fit all, we offer many different ways to meet your math goals depending on your student.

My son found the transition from Singapore Math 6A/6B to Principles of Mathematics to be seamless.

This past year my third son used Principles of Mathematics Book 2 after exiting Singapore 6A/6B, and it worked well! He went into Principles of Mathematics Book 2 right after Singapore 6A/6B without ever doing Principles of Mathematics Book 1. The transition was seamless even though the programs are different. We had a good year with some concepts being very easy, and others being a bit harder.

Even for a strong math student, Foerster’s Algebra I is better saved for a student’s freshman year.

Even though your son is good at math, you’re right, Foerster’s Algebra is better saved for a student’s freshman year. It would be a challenge to do Foerster’s Algebra I as an 8th grader. It is a wonderful course, but it is also very rigorous. The problem-solving that makes Foerster’s math stand out also requires a more mature student to process what is being asked. So, having a bit more maturity on one’s side before heading into Foerster would be a bonus.

Principles of Mathematics Book 2 provides a good transition from Singapore Math 6A/6B to high school Algebra 1.

If you have an 8th grader coming out of 6A/6B successfully, I’d suggest doing Principles of Mathematics Book 2 next. Then, you could begin either VideoText, Foerster’s Algebra 1, or No-Nonsense Algebra as a freshman. This would help your student firm up any needed skills, making the transition to Algebra smoother in the long run. It would also make the 8th grade year less intense math-wise. Ultimately, this path will give your student a great foundation for the rigor of the math coming in high school!

Blessings,

Carrie