Mental Math of 45 x 25

Wow. I suck at this #MTBoS30 thing.

Couple days ago I tweeted this out because my kids were working on the same one.

Thousands of folks — okay, maybe 7 or so people — responded, and I thought it’d be fun to see what some common and not-so-common strategies were.

Most common (22 people):

(40 x 25) + (5 x 25)

or

(4 x 25 x 10) + (5 x 25)

Second most common (11 people):

(45/4) x 100

or

(45/2)/2 x 100

Tied with 6 people for each strategy:

(45 x 100)/4

(45 x 2 x 10) + (45 x 5) = 900 + 225

Equally popular with 4 nods each:

(50 x 25) – (5 x 25)

(40 x \$0.25) + (5 x \$0.25) = \$11.25 –> Change to 1125

4 quarters = \$1 –> so 44 quarters \$11 –> plus extra quarter = \$11.25 –> so, 1125

Still others:

35² – 10²

(100 x 25)/2 – (5 x 25)

40 quarters + 5 quarters = 1,000 cents + 125 cents

(9 x 5) x (5 x 5) = 9 x 5³ = 9 x 125 = (10 x 125) – 125 = 1250 – 125

45² – (45 x 20) = 2025 – 900

25² + (20 x 25) = 625 + 500

doubling and halving: (45/2) x (25 x 2) = 22.5 x 50 = 11.25 x 100

And an area model from Mylene:

Yay to math tallks! Also, I think it’s really important that we are intentional about what numbers we give students for mental math. Jason Zimba once said, “Think of mental calculation as being the best approach only in cases where a readily apparent mental strategy is probably both faster and more reliable than the standard vertical written algorithm.”