Math logic Guide

Rounding Rule

THE RULE: Look at the first digit to the right of your target.

·         0–4: "Stay low" (Keep the target digit as is).

·         5–9: "Go high" (Add 1 to the target digit).

THE "STOPPING" POINT (The Target):

·         For Percentages: Stop at the whole number (e.g., 22.37% 22%).

·         For Money: Stop at the hundredths place (e.g., $4.0247 $4.02).

Choosing the Right Operation

• Concept: Choosing the Math

• HAVE: "How much did it change?" $\rightarrow$ Subtraction (Absolute Change).

• HAVE: "What percent did it change?" $\rightarrow$ Division (Relative Change).

• HAVE: "How many hours of work to buy this?" $\rightarrow$ Division (Proportional Reasoning).

Math Anxiety

• HAVE: What numbers do I see? (The two indexes and the dollar amount, if there is one).

• WANT: What is the question asking for? (A comparison or a new price?)

The "Flip" Check: If the math results in a number that doesn't make sense (like an index value smaller than 1, or a rent price that dropped by thousands), look at your fraction. Did you put the "New" year on top

"Percent Change" (Absolute & Relative)

• Absolute Change (The Gap): New Total - Starting Amount = Dollar Amount

• Relative Change (The Extra %): Gap/Starting Amount) * 100 = Percent Extra

• All In One (New Value – Starting Value) / Starting Value x 100 = Relative Change

"How many times bigger?" (Ratio)

·       Action: New Total/Starting Amount

·        Result: The ratio (e.g.,1.25).

"What percent of...?" (Total)

• ·  Goal: Turn any "new vs. old" relationship into a total percentage.

  ·  Action: 1. Divide the New Total by the Starting Amount.

  2. Multiply the result by 100.

• (New Total / Starting Amount) x 100

"What percent MORE than...?" (Increase)

·   Action: (New Total/Starting Amount) x 100

·  Result: The "extra" percentage (e.g., 25%).

The "Adjusting" Pattern (Updating a Price)

·         Goal: Updating a dollar amount (like a wage or rent) to a new year.

·         The Recipe: Take the Original Price and multiply it by that same "multiplier" (New Index / Old Index).

·         Why: You are just applying that inflation growth to a specific dollar amount to see what it would be worth today.

·         If the question is "How much is $0.25 worth now?", use the Adjusting.

How do I handle math modules that feel like a 'trick' or a chain of confusing questions?"

The "Chain Reaction" Strategy:

·  Keep Your Master Key: Write down your first answer (the ratio or constant) on paper. You will need it!

·  Follow the Ripple Effect: When the question changes (e.g., from "Ratio" to "Percent"), don't start over. Apply your Master Key to the new request.

·  One Story, Multiple Steps: Treat parts (a), (b), and (c) as a single, ongoing calculation, not separate problems.

Decimal Places

• 1st spot (.x): Tenths

• 2nd spot (.xx): Hundredths

• 3rd spot (.xxx): Thousandths

• 4th spot (.xxxx): Ten-thousandths