Properties of Multiplication

Dear Families,

Your child is learning special rules (called properties) that make multiplication easier. These aren't just rules to memorize - they're powerful strategies that help solve harder problems! The activities below use everyday situations to practice these math "shortcuts."

Why This Matters for the FAST Test

The Florida FAST assessment asks students to identify properties AND use them to solve problems. The most important property is the distributive property, which lets students break apart hard problems like 7 × 14 into easier parts: 7 × 10 + 7 × 4. Students who master this can solve two-digit multiplication mentally!

Quick Reference: The 5 Properties

Commutative: Order doesn't matter. 3 × 5 = 5 × 3
Associative: Grouping doesn't matter. (2 × 3) × 4 = 2 × (3 × 4)
Distributive: Break it apart! 6 × 12 = (6 × 10) + (6 × 2) = 60 + 12 = 72
Identity: Times 1 stays the same. 8 × 1 = 8
Zero: Times 0 equals 0. 9 × 0 = 0

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Activity 1: Grocery Store Break-Apart

Use the distributive property while shopping

Find an item with a "teen" number price (like 13, 14, 15 cents per unit).
Decide how many to "buy" (use a single digit like 3, 4, or 5).
Challenge your child: "If apples are 14 cents each and we get 5, what's the total?"
Have them break it apart: 5 × 14 = 5 × 10 + 5 × 4 = 50 + 20 = 70 cents
Check with a calculator or by counting!

Example: "Bananas are 12 cents each. We're getting 6. Can you figure it out without a calculator?"
6 × 12 = 6 × 10 + 6 × 2 = 60 + 12 = 72 cents

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Activity 2: Array Hunt at Home

Find arrays and practice the commutative property

Hunt for arrays (things arranged in rows and columns) around the house: egg cartons, muffin tins, window panes, tiles, keyboard keys.
Count the rows and columns. "This egg carton has 2 rows and 6 columns."
Write both multiplication facts: 2 × 6 = 12 AND 6 × 2 = 12
Rotate the item (or imagine rotating it). "Now it's 6 rows and 2 columns - but still 12!"
That's the commutative property - order doesn't change the answer!

Extension:

For a muffin tin (often 3 × 4), ask: "If we had 3 muffin tins, how would you find the total muffins?" This leads to 3 × 12 = 3 × 10 + 3 × 2 (distributive property again!)

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Activity 3: Smart Grouping Game

Practice the associative property with mental math

Give your child three small numbers to multiply: 2 × 4 × 5
Ask: "Which two numbers would YOU multiply first? Why?"
Show that grouping smartly makes it easier:
- (2 × 4) × 5 = 8 × 5 = 40
- 2 × (4 × 5) = 2 × 20 = 40 (Easier because 4 × 5 = 20!)
Try more: 5 × 3 × 2, 4 × 5 × 2, 2 × 6 × 5
The trick: Look for pairs that make 10 or other easy numbers!

Challenge: 5 × 7 × 2
Smart grouping: 5 × 2 = 10, then 10 × 7 = 70
Much easier than 5 × 7 = 35, then 35 × 2!

Questions to Ask Your Child

"If I know 8 × 6 = 48, what's another fact I automatically know?" (6 × 8 = 48)
"What happens when you multiply any number by 1? By 0?"
"How would you solve 7 × 12 in your head without memorizing it?"
"If there are 0 bags with 25 marbles each, how many marbles? Why?"
"Which is easier to calculate: 8 × 5 × 2 or (8 × 5) × 2 or 8 × (5 × 2)? Why?"

Resumen en Espanol

Propiedades de la multiplicacion: Su hijo esta aprendiendo reglas especiales que hacen la multiplicacion mas facil. Estas son estrategias poderosas para resolver problemas.

Las 5 propiedades:

Conmutativa: El orden no importa. 3 × 5 = 5 × 3
Asociativa: La agrupacion no importa. (2 × 3) × 4 = 2 × (3 × 4)
Distributiva: Separar en partes. 6 × 12 = (6 × 10) + (6 × 2) = 72
Identidad: Multiplicar por 1 da el mismo numero.
Cero: Multiplicar por 0 siempre da 0.

Actividades: Practiquen la propiedad distributiva en la tienda. Busquen arreglos (filas y columnas) en casa. Jueguen a agrupar tres numeros de la manera mas facil.

Home Activity: Properties of Multiplication