Math Reference Sheets: What's Changed and Where Can I Get Them?
Math Reference Sheets: What's Changed and Where Can I Get Them?
September 12, 2022|Education, Florida, B.E.S.T. Standards, Florida's Standards, Math, Testing
B.E.S.T. & F.A.S.T. Math Reference Sheets
In Florida, students in grades 4 through 8 and for those enrolled in high school Algebra and Geometry have math reference sheets available to them when they take the new F.A.S.T. math assessment. This is nothing new; those same students had reference sheets available in the past, too.
So, what's the big deal?
The new F.A.S.T., which assesses our new B.E.S.T. standards, has some KEY changes that are reflected in the new reference sheets. For that reason, teachers, students, leaders, and parents all need to be aware of what's new and what's not.
What's Changed?
What's the same?
Free Download 22-23 F.A.S.T. Math Reference Sheets from Uncomplicate Ed
Sounds great, so where do where can we download the new reference sheets?
We asked the same thing, but we were unable to find them on any site from the FLDOE. They are currently only found in the practice sites IN the actual F.A.S.T. tests.
Don’t worry though - we have uncomplicated it for you! We compiled them one-by-one for you from the F.A.S.T. testing site so that you can use them in your classrooms now. Click HERE to download your free reference sheets for the new F.A.S.T..
Let's break down some of these changes grade-level by grade-level.
NOTE: These go very in-depth. Feel free to scroll straight to the grade-level(s) that is pertinent to you.
4th Grade
Comparison of 4th Grade Math Reference Sheet Old (FSA) to New (F.A.S.T.)
The Conversions - 4th grade
In 4th grade, the changes from FSA to F.A.S.T. regarding the conversions have items that were removed, not added. Here are the list of conversions removed:
miles to feet and miles to yards
cups to ounces
tons to pounds
days to hours, years to days, and years to weeks
Why? Take a look below at the 4th grade benchmark for measurement.
From Florida's B.E.S.T. Standards for Mathematics
And this excerpt under the Purpose and Instructional Strategies section of the 4th grade B1G-M.
From 4th Grade B1G-M, MA.4.M.1.2, Purpose and Instructional Strategies
Now we can see why some extraneous information was removed. It will be key for teachers to use this reference sheet when working with measurement in class (math AND science).
The Formulas - 4th Grade
Comparing 4th Grade Formulas: Before (FSA) to After (F.A.S.T.)
Labeling the formula, providing a key, and making the formats more grade-appropriate. What an upgrade!
I think I just heard you yell “THANK YOU!” all the way from here. Not only does the key provide grade-level proper help with the formulas but look at the formulas themselves.
It flat out states that the formula is for a “rectangle.” Thank you!
It provides an appropriate representation of the formulas for 4th grade. For example, for finding the perimeter of a rectangle, it shows 4 addends (l + l + w + w) instead of using coefficients (2l + 2w). Thank you!
And for area, they’ve provided students with the much more appropriate symbol for multiplication at this grade, “x” instead of the two variables side by side (lw) – something not used until later grade levels. Thank you!
Again, THANK YOU! This is a big win for our 4th grade students.
5th Grade
Comparison of 5th Grade Math Reference Sheet Old (FSA) to New (F.A.S.T.)
The Conversions - 5th grade
Unlike 4th grade, 5th grade has some items that have been removed, and some that have been added. Let's break it down.
Added:
centimeters to milliliters
weeks to days
Removed:
liters to milliliters
grams to milligrams and kilograms to grams
years to days, and years to weeks
When looking at the 5th grade benchmark for this skill, we can see that, like 4th grade, the benchmark explicitly states that conversions should not be memorized. We can also see that students are to use their knowledge of multiplication to solve some of the conversions that were removed.
From Florida's B.E.S.T. Standards for Mathematics
The Formulas - 5th Grade
Comparing 5th Grade Formulas: Before (FSA) to After (F.A.S.T.)
That is not a typo or mistake in publishing this post. The old reference sheets for 5th grade had NO support with formulas. Now students have the formulas for both perimeter and area of a rectangle, as well as for the volume of a rectangular prism. And, like 4th grade, it has provided students with a Key and grade-appropriate equations.
5th Grade Students Now Have Formulas for:
Area of a rectangle
Perimeter of a rectangle (in 2 different ways)
Volume of a rectangular prism (in 2 different ways)
This is incredibly helpful for our 5th graders.
6th Grade
Comparison of 6th Grade Math Reference Sheet Old (FSA) to New (F.A.S.T.)
The Conversions - 6th grade
6th Grade only has one minor change in terms of their conversions, and that's under the time category:
Added:
weeks to days
Why are there fewer changes to the conversions beginning in 6th grade? Because Measurement is no longer a strand after 5th grade.
The Strands from Florida's B.E.S.T. Standards for Mathematics
The Formulas - 6th Grade
Comparing 6th Grade Formulas: Before (FSA) to After (F.A.S.T.)
Again, we are grateful that they are labeling the formulas as well as providing students with a Key for solving the problems.
But, wait, we lost some formulas?
Rectangles and Triangles
Yes, the formulas for area are gone. Why? In 6th grade students are expected to recall the area of a rectangle AND use their knowledge of the area of a rectangle to derive the area of a triangle and to "know [it] from memory." Take a look at the 6th grade benchmark:
From Florida's B.E.S.T. Standards for Mathematics
For that reason, the formulas for the area of a rectangle and the area of a triangle have been removed from the 6th grade reference sheet.
Trapezoids
The same is true for why the formula for the area of a trapezoid is removed. Take a look at the next 6th grade geometry benchmark:
From Florida's B.E.S.T. Standards for Mathematics
Because trapezoids can be composed into rectangles and triangles, students do not need, nor would it be appropriate to use the formula for the area of a trapezoid. However, students specifically needing to derive the formula for the area of a trapezoid does appear in 7th grade (MA.7.GR.1.1).
7th Grade
Comparison of 7th Grade Math Reference Sheet Old (FSA) to New (F.A.S.T.)
And the award for most changes to their math reference sheet goes too....7th grade!
Yes, there are several changes to the 7th grade math reference sheet, so buckle in, let's go for a ride.
The Conversions - 7th grade
Like 6th grade, customary, metric, and time conversions had little change (only the same) addition of weeks to day. However, in 7th grade, we get an entirely new category for conversions: Conversions Between Systems.
Comparing 7th Grade Conversions Between Systems: Before (FSA) to After (F.A.S.T.)
Again, not a typo. While both the old and the new still provide customary conversions within a system of measure, FLDOE has provided students in 7th (and 8th) grade(s) this year with conversions between systems of measure. This is incredibly helpful for our students since solving real-world problems with proportions hits center stage in this grade level.
The Formulas - 7th Grade
Comparing 7th Grade Formulas: Before (FSA) to After (F.A.S.T.)
I know, right? The support given to our students with this change is incredible.
Formulas are labeled.
A Key is provided.
Interest and Percent formulas have been added.
But why did one of the formulas for volume and both of the formulas for surface area disappear?
This takes some breaking down.
Transition Guide: Topics No Longer in 7th Grade
Removed
The Formula for the Volume of a Rectangular Pyramid (V = 1/3 Bh)
This one has a simple answer. The entire CONCEPT has moved out of 7th grade altogether. This is now expected in the Geometry High School course.
Removed
The Formulas for the Surface Area of a Rectangular Prism (SA = Ph + 2B) and Rectangular Pyramid (SA = ½ Pl + B)
The answer as to why these formulas have been removed is found in the 7th grade B1G-M (Best Instructional Guide for Mathematics) under the Purpose and Instructional Strategies for MA.7.GR.2.1.
Excerpt from 7th Grade B1G-M for MA.7.GR.2.1
Basically, it is telling us that students are still expected to be able to derive the formula and/or solution to the surface area of 3-D figures by using a figure’s net. Therefore, they will not be providing the formula on the reference sheet.
There are some NEW formulas. What are those about?
Added
Simple Interest Formula
New: Simple Interest Formula added to 7th Grade Reference Sheet
While the addition of the Formula for Simple Interest is new to the reference sheet, the skill of solving for simple interest is not new to 7th grade. In the previous MAFS standards, the content limits and test item specifications did not state whether the formula had to be memorized or not. Because it was then assumed to be memorized (or derived), it was not included on the previous reference sheet.
However, with the new B.E.S.T., you’ll find it explicitly stated under the Purpose and Instructional Strategies in the 7th grade B1G-M for this benchmark that it is NOT intended to be memorized. ()
MA.7.AR.3.1: Apply previous understanding of percentages and ratios to solve multi-step real-world percent problems
Excerpt from 7th Grade B1G-M for MA.7.AR.3.1
Added
Percent Error Formula and Percent Change Formula
Like Simple Interest from above, students were asked to solve for percent error as well as percent change with the previous 7th grade MAFS. And again, the former item specifications did not state that the formulas needed to be memorized (or not).
However, dissimilar to Simple Interest from above, the new B1G-M does NOT explicitly state that the percent error and change formulas should be provided nor is there any mention of memorization. Nevertheless, because they have been provided on the reference sheet, it looks like this is another set of formulas that we are providing to help our students be more successful.
Difference in wording Percent formulas from the reference sheet to the B1G-M
CAUTION!!! Did you notice the language change from the reference sheet to the B1G-M?
For Percent of Change, the reference sheet uses the terms “final value” and “initial value” whereas the B1G-M uses the terms “new price” and “original price.” It also refers to this formula as “Percent Increase/Percent Decrease” rather than “Percent Change.” Our suggestion? Use the terms interchangeably in your classroom. Certainly, the terms from the reference sheet are of higher-level vocabulary, and our students are more than capable of using the more specific academic language.
Transition Guide: New Topics to 7th Grade
Added
Right Circular Cylinders
But wait, there’s more? This is the last change with the 7th grade math reference sheet. The new reference sheet provides students with the formula for finding the volume of right circular cylinders.
This is new to the reference sheet, because it’s new to the course!
Also note that students will be asked to find the surface area of right circular cylinders, but it is not provided as a formula, because, once again, students must be able to find the surface area of 3-D figures when given a net (referenced above with rectangular prisms and pyramids).
7th Grade Math Benchmark showing surface area From Florida's B.E.S.T. Standards for Mathematics
8th Grade
Comparison of 8th Grade Math Reference Sheet Old (FSA) to New (F.A.S.T.)
The Conversions - 7th grade
Yes, this is EXACTLY the same as 7th grade in terms of conversions. So, to quote ourselves from above:
Comparing 8th Grade Conversions Between Systems: Before (FSA) to After (F.A.S.T.)
While both the old and the new still provide customary conversions within a system of measure, FLDOE has provided students this year with conversions between systems of measure. This is incredibly helpful for our students!
The Formulas - 8th Grade
Comparing 8th Grade Formulas: Before (FSA) to After (F.A.S.T.)
That's right. Whereas before with MAFS and FSA, 8th graders were not provided with ANY formulas for reference, now we have both formulas and theorems to help our students reach success.
Let’s break these down.
New: Slope Formula added to 8th Grade Reference Sheet
Added
Slope Formula
Like the 8th grade MAFS/FSA of prior years, students were expected to “derive” the formula for finding the slope. However, in B.E.S.T., the FLDOE has been much more explicit that students are not expected to, nor is it developmentally appropriate for pre-Algebra students (i.e., 8th grade math students) to have this formula both derived AS WELL AS memorized by the end of the year.
Therefore, it is provided for them on the F.A.S.T. reference sheet.
For an example of the explicit language of B.E.S.T., look at just one instance where the derivation (and multiple formats) for finding slope is mentioned.
MA.8.AR.3.3: Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form.
Excerpt from 8th Grade B1G-M for MA.8.AR.3.3
New: Triangle Inequality Theorem added to 8th Grade Reference Sheet
Added
Triangle Inequality Theorem
The understanding and application of the Triangle Inequality Theorem is NEW to 8th grade with B.E.S.T. It moved from 7th grade with MAFS to 8th grade with B.E.S.T. However, the Theorem wasn’t provided on the old 7th grade reference sheet either.
Transition Guide: New Topics to 8th Grade
So if the theorem wasn’t provided on the 7th FSA before, why is it included on the 8th F.A.S.T. now?
Again, it all comes back to students applying understandings to derive formulas, specifically, the Pythagorean Theorem (for which the formula DOES have to be memorized).
Because they want student to use the Triangle Inequality Theorem and recall from memory the Pythagorean Theorem, they have provided the former on the reference sheet, and left off the latter.
8th Grade Geometry Benchmarks from Florida's B.E.S.T. Standards for Mathematics
New: Triangle Sum Theorem added to 8th Grade Reference Sheet
Added
Triangle Sum Theorem
The triangle sum theorem is mentioned only in benchmark MA.8.GR.1.5 in both the clarification and the purpose and instructional strategies. See the screenshots below from the B1G-M. Of note, the Triangle Sum Theorem was never mentioned in neither the 7th or 8th grade former MAFS, nor the former Geometry course MAFS. In other words, this is a new concept for our students to learn and our teachers to teach.
Notice that it’s calling upon the work and learning that happened in 4th and 5th grades with B.E.S.T.!
Excerpt from 8th Grade B1G-M for MA.8.GR.1.5
In our next post, we'll talk about meaningful ways to integrate the reference sheets into your daily classroom. Stay tuned!
Resources and Links
Download your math reference sheets HERE.
Download your formulas icon HERE.
Click HERE to download consolidated manuals from our store.
Click HERE to go the the B.E.S.T. Assessments page from the FLDOE.
Click HERE to be taken to the FLDOE page for math.
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For B.E.S.T. training for your school, check out our website or contact me directly. We’ve been helping schools all over the state, and would love to help your school be ready for the B.E.S.T. and the F.A.S.T.
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