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Fun POW
One day in math class Mia invented a problem for her classmates to solve. She said, "My mom’s and dad’s ages are 3 years apart. I’m exactly 1/4 of my mom’s age, and I’m 24 years younger than Dad. How old am I?"
Mia was surprised when her classmates came up with two different ages that fit her clues.
What answers did her classmates find?
Explain how you solved the problem. Show how you know both answers are correct.
Extra: Suppose that Mia is 1/3 of her mother's age. Find two other numbers to replace the differences of 3 and 24 that still result in two possible ages for Mia.
I notice
Mia's parents are 3 years apart
Mia is 24 years younger than her dad.
That it only says three years apart not above or below.
That her classmates found two different answers.
I wonder
What the Mom and Dads ages were.
If the Dad was older or younger.
If the mom or dad is older
If her mom is 3 years older or 3 years younger.
How old her parents are.
Patterns – The Problems
January 11, 2010
Janie is using identical sticks to create a chain of diamonds. If she creates 1 diamond (figure 1), she uses 4 sticks. If she creates a 3-diamond chain (figure 3), she uses 10 sticks. How many sticks would be needed to create a 46-diamond chain?
Danny - I wonder how many sticks she will need.
Danny - I notice that she uses 4 sticks to create 1 diamond.
Mia - I wonder what the length of each side of the diamond will be.
Mia - I notice she uses 10 sticks to make a 3 diamond chain. ----
Tracie is making a pattern using circles, as shown below. The first figure uses 1 circle and contains 1 “individual” space (an individual space is a space that is not divided into smaller spaces by other circles), while the third figure uses 3 circles and contains 7 individual spaces. How many individual spaces are contained in the figure that uses 12 circles?
----
How many circles would Tracie need to use to create a figure with 175 individual spaces?
Fun POW
One day in math class Mia invented a problem for her classmates to solve. She said, "My mom’s and dad’s ages are 3 years apart. I’m exactly 1/4 of my mom’s age, and I’m 24 years younger than Dad. How old am I?"
Mia was surprised when her classmates came up with two different ages that fit her clues.
What answers did her classmates find?
Explain how you solved the problem. Show how you know both answers are correct.
Extra: Suppose that Mia is 1/3 of her mother's age. Find two other numbers to replace the differences of 3 and 24 that still result in two possible ages for Mia.
I notice
Mia's parents are 3 years apart
Mia is 24 years younger than her dad.
That it only says three years apart not above or below.
That her classmates found two different answers.
I wonder
What the Mom and Dads ages were.
If the Dad was older or younger.
If the mom or dad is older
If her mom is 3 years older or 3 years younger.
How old her parents are.
Patterns – The Problems
January 11, 2010Janie is using identical sticks to create a chain of diamonds. If she creates 1 diamond (figure 1), she uses 4 sticks. If she creates a 3-diamond chain (figure 3), she uses 10 sticks. How many sticks would be needed to create a 46-diamond chain?
Danny - I wonder how many sticks she will need.
Danny - I notice that she uses 4 sticks to create 1 diamond.
Mia - I wonder what the length of each side of the diamond will be.
Mia - I notice she uses 10 sticks to make a 3 diamond chain.
----
Tracie is making a pattern using circles, as shown below. The first figure uses 1 circle and contains 1 “individual” space (an individual space is a space that is not divided into smaller spaces by other circles), while the third figure uses 3 circles and contains 7 individual spaces. How many individual spaces are contained in the figure that uses 12 circles?
----
How many circles would Tracie need to use to create a figure with 175 individual spaces?