A local nursery is discounting shrubs and bushes. A 1-foot diameter shrub is only $1. A ½-foot diameter shrub is $2. The ¼-foot diameter shrub is $4. (And so on… one-third foot diameter = $3, one-tenth foot diameter = $10.) What is the cheapest way to fill the greatest area of a flowerbed that is a 4-foot square? How much… Read more →
If my purchase at the store totals $4.97 and I pay with a $5 bill, I get 3 coins back. If I give the cashier a $5 bill plus two pennies, I get 1 coin back. How can I use this transaction to consolidate my change into the fewest coins possible? When should I give the cashier a few extra… Read more →
I love those rich conversations with colleagues when they express a thought and you feel like you agree completely, but you’ve never been able to express it that clearly. That’s how Routines for Reasoning makes me feel – the book explores strategies teachers can employ to help develop students’ reasoning and problem-solving abilities. Each of the strategies does such a… Read more →
A new Mondo-Lotto Lottery Game is a scratch-off ticket with a three-by-three grid. Each section has an X or an O – just like Tic-Tac-Toe. If you scratch off the same three symbols in any row, column, or diagonal, you win a prize. What is the fewest number of sections you might have to scratch off to know your ticket… Read more →
Twelve is the largest number that is only one syllable long. “Twenty-four” is three syllables, but so is “eight times three,” which is also equal to twenty-four. What is the greatest value expression or number you can write with five syllables? What is the smallest value you can create with five syllables? Can you create an expression whose value is… Read more →
Twitter-Length Tasks can be quickly and simply explained, yet allow for extensive exploration. Both hands of a clock are constantly moving. The small hour hand only points directly at a number when it is the top of the hour. Otherwise, that hour hand keeps moving around. So at 7:30, the hour hand is halfway between 7 and 8. So at 3:00,… Read more →
Twitter-Length Tasks can be quickly and simply explained, yet allow for extensive exploration. In the equation 4 + 6 = 10, each number is written in alphabetical order: four + six = ten In the equation 3 – 1 = 2, the numbers are not in alphabetical order: three – one = two Can you come up with one example of… Read more →
Twitter-Length Tasks can be quickly and simply explained, yet allow for extensive exploration. Draw six dots. A line segment that connects two dots is worth 1 point – as long as it doesn’t intersect any other line segments. A line segment with one intersection is worth ½ a point, a line segment with two intersections is worth ¼ a point, three… Read more →
Twitter-Length Tasks can be quickly and simply explained, yet allow for extensive exploration. Use one cut to make a square into 2 pieces. What types of shapes are possible? (Two Rectangles, two trapezoids, a triangle and a trapezoid, what else?) How many different types of shapes can you create if you used 2 cuts to divide the square? Is the answer… Read more →
Twitter-Length Tasks can be quickly and simply explained, yet allow for extensive exploration. Draw a line segment inside a square the stretches all the way to the edges of the square.Draw an intersecting line segment. Draw another line segment so that each line only has one intersection point inside the square.How many line segments can you add to the square making… Read more →