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How are grades calculated using horizontal and vertical roll-up in standards-based grading?

Prerna Singh

Last edited 99 days ago by Prerna Singh.

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In standards-based grading, final grades are calculated using a combination of horizontal and vertical roll-up calculations. These methods ensure that both individual standard scores and parent standard scores are considered when deriving a final grade.

Types of calculations in standards-based grading

Toddle uses two roll-up methods to derive ratings of individual and parent standards:

Horizontal calculation

When a student has been evaluated multiple times on the same learning standard, horizontal calculation is applied to combine those evaluations into a single score for that standard. Toddle supports the following calculation methods:

Most recent score: Uses the latest rating to reflect recent performance

Decaying average: Weighs recent scores more heavily than older ones

Mean (average): Averages all ratings equally. Best used when all tasks carry a similar weight

Weighted mean: Assigns a fixed weight (provided by you) to the most recent rating while averaging the rest

Mode: Picks the most frequently occurring rating

Maximum value: Takes the highest score achieved

Weighted mean: Assigns a fixed weight to the most recent rating (as defined by you), while distributing the remaining weight evenly across earlier ratings.

Power law: Uses a mathematical formula to predict a student’s final performance based on their learning trend. It gives more weight to recent ratings but still considers earlier ones.

Example-

Let’s take an example of the standard “Predicting what might happen next in a text based on the cover, title, and illustrations(R2)” assessed for Alex Peirera.

Scores from tasks:

Literary analysis: 7

Dystopia: 3

Common Character Archetypes in Dystopia: 7

Selected aggregation method: Mean

Calculation: (7+3+7)/3=5.7

So, the final score for this strand is 5.7.

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Vertical calculation

Once individual standards have a single score (post-horizontal roll-up), the vertical roll-up aggregates these into a rating for the parent standard.

Toddle supports the following calculation methods:

Mean: Average scores across all child standards. Most balanced method.

Maximum value: Uses the highest score among child standards.

Rollup weighting: Calculates the parent standard’s grade by combining child standard scores with different weights, as configured by the school.

The method used to roll up child standard scores may vary depending on the type of grade scale selected. Let’s explore how this works with different types of grade scales.

When using a Numeric grade scale

1. Numeric grade scale that uses numeric values

If you're using a numeric grade scale that uses numeric values for calculation, Toddle uses the actual scores directly to calculate the parent score. It doesn't convert them into grade values.

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Let’s look at the parent standard Reading (R) for Alex. It includes the following child standards and their corresponding scores:

R2: 5.7

R3: 5.7

R6: 6.0

R7: 7.0

R8: 6.0

R9: 5.0

Since this grade scale uses numeric values, the actual scores are used as is as, without converting them into grade values.

The selected roll-up method (in this case, Mean) and any assigned weights are then applied to calculate the parent score.

If weights are equal: (5.7+5.7+6.0+7.0+6.0+5.0)/6=5.9

Since R1 is the only child under Reading (R), its score (5.9) becomes the final score for the parent standard Reading (R).

So, the vertical roll-up for the Reading (R) strand is 5.9.

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2. Numeric grade scale that uses grade values

If you're using a numeric grade scale that uses grade values, Toddle converts the scores of child standards into grade values to calculate the score for the parent standard.

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Let’s look at the parent standard Reading (R) for Alex. It includes the following child standards and scores:

Scores on individual strands

Mapped grade value

R2: 4

R3: 3

R6: 4

R7: 5

R8: 4

R9: 5

There are no rows in this table

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Since this grade scale uses grade values, the actual scores are converted into grade values.

The selected roll-up method (in this case, Mean) and any assigned weights are then applied to calculate the parent score.

If weights are equal:

Mean = (70+60+70+90+70+90)/6=75

75 falls in the 4 band in the 1-5 grade scale.

Since R1 is the only child under Reading (R), its score becomes the final score for the parent standard Reading (R).

So, the vertical roll-up for the Reading (R) strand is 4.

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When using an Alpha grade scale

If you're using an alpha grade scale (A–F), Toddle uses the grade values mapped to each letter to calculate the parent score.

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Let’s look at the parent standard Reading (R) for Alex. It includes the following child standards and scores:

Scores on individual strands

Mapped grade value

R2: A

R3: B

R6: C

R7: A

R8: B

R9: B

There are no rows in this table

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The selected roll-up method (in this case, Mean) and any assigned weights are then applied to calculate the parent score.

If weights are equal:

Mean = (85+70+55+85+70+70)/6=72.5 (73)

73 falls into the B band in the A–F scale.

Since R1 is the only child under Reading (R), its score becomes the final score for the parent standard Reading (R).

So, the parent standard is graded as B.

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Final grade calculation for a course/subject

The final grade for the subject/course is derived by aggregating the ratings of all parent standards across one or more standard sets.

Here’s how Toddle handles the logic:

You can select one or more grade scales at the final grade level

You can also select one or more standard sets, and each of these may be mapped to their own grade scales

Toddle uses the grade scale, along with the horizontal and vertical calculation methods defined in each standards set, to calculate ratings for its child and parent standards.

Then it uses the selected final grade scale(s) to derive the final course/subject grade(s)

Let’s understand this with two examples:

Example 1: When standard sets are mapped to a numeric grade scale

Final grade scale selected: A–F

Calculation method: Standards-based grading

Selected standard sets:

For A-F grade scale: Missouri Learning Standards – English Language Arts (1–8 scale) and New Brunswick Curriculum – English (1–8 scale)

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Students are being rated on two standard sets. Each standard set (e.g., Missouri Learning Standards, New Brunswick Curriculum) contains multiple child standards assessed using a 1–8 numeric scale. The final grade is derived through both horizontal and vertical calculations:

1. Horizontal calculation:

For each individual standard, scores from all linked evaluations are combined using the selected method (such as mean). For example, if an individual standard has three evaluation scores 7, 3, and 7, the mean would be 5.7.

2. Vertical calculation:

Once all child standards are scored, Toddle rolls them up to the parent standard level (using the chosen roll-up method (in this case, Mean). This vertical roll-up happens within each standard set independently.

For example, for Alex Peirera:

Missouri standard Reading = 5.9

New Brunswick standard Speaking and Listening = 6.0

3. Final grade calculation:

Once Toddle calculates the parent standard scores for each standard set, it computes the course/subject-level score using mean roll-up method.

For example, for Alex Peirera:

Missouri standard set: Reading = 5.9

New Brunswick standard set: Speaking and Listening = 6.0

Course-level score = (5.9 + 6.0) ÷ 2 = 5.95

This final numeric score (5.95) on a 1-8 grade scale is then converted into a percentage: (5.95÷8)×100=74.37%

Toddle maps this percentage against the configured A–F scale cutoff values to calculate the final grade:

70 or higher = Grade B

85 or higher = Grade A

So, Alex’s final percentage of 74.37% maps to Grade B on the A–F scale.

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Example 2: When standard sets are mapped to an alpha grade scale

Final grade scale selected: A–F

Calculation method: Standards-based grading

Selected standard sets:

For A-F grade scale: Missouri Learning Standards – English Language Arts (A-F scale) and New Brunswick Curriculum – English (A–F scale)

Students are being rated on two standard sets. Each standard set (e.g., Missouri Learning Standards, New Brunswick Curriculum) contains multiple child standards assessed using an A-F scale. The final grade is derived through both horizontal and vertical calculations:

1. Horizontal calculation:

For each individual standard, scores from all linked ratings are combined using the selected method (such as mean). Since the grade scale is alphabetical, Toddle first converts each grade into its mapped numeric grade value before performing the calculation.

For example, if a student receives two ratings: A (85) and B (70), Toddle calculates it as: (85 + 70)/2 = 77.5, which then maps back to a B on the A–F scale.

2. Vertical calculation:

Once all child standards are evaluated, Toddle rolls them up to the parent standard level (using the chosen roll-up method (in this case, Mean). This vertical roll-up happens within each standard set independently.

Toddle uses the raw numeric scores (converted from individual ratings) of each child standard to calculate the parent standard score using the selected roll-up method. The final result is then mapped back to the A–F grade scale to display the parent grade.

For example, for Alex Peirera:

Standard set 1: Missouri standard- Reading

Mean = (77.5+70+85+85+70+70)/6 =76.25

which falls between 70–84 → Grade = B

Standard set 2: New Brunswick – Speaking and Listening

Mean = (85 + 85 + 85 + 85 + 85 + 85)/6 = 85

which maps to Grade = A

3. Final grade calculation:

Once Toddle calculates the parent standard scores for each standard set, it computes the course/subject-level score using the mean roll-up method.

For example, for Alex Peirera:

Missouri standard set: Reading = 76.25 (B)

New Brunswick standard set: Speaking and Listening = 85 (A)