Stuck? Start here. Read the steps, try the problem, then check your answer.
I can…
I can find patterns and pattern rules, use them to make generalizations, and check my solutions with a table of values.
Key words
pattern — Something that repeats or changes in a predictable way.
pattern rule — The instruction that tells how to get from one number in a pattern to the next.
generalization — A statement that is true for a whole pattern, made by noticing repeated calculations.
table of values — A table that lists each step of a pattern so you can check that a solution is reasonable.
reasonableness — Whether an answer makes sense — checked as you work, with adjustments made when needed.
Steps
A change jar is full of pennies, nickels, dimes, and quarters worth $53.50 in total. How many of each coin could there be?
Each penny has a value of $0.01, so 100 pennies have a value of $1.00.
Each nickel has a value of $0.05, so 100 nickels have a value of $5.00. Each dime has a value of $0.10, so 100 dimes have a value of $10. Each quarter has a value of $0.25, so 100 quarters have a value of $25.
I multiply the number of each coin by its value. And I notice a generalization: because the jar's total, $53.50, ends in 0, the number of pennies can only be a multiple of 5.
Try it
Ana is laying stepping stones along a garden path, and each new section of the path adds the same number of stones. Which way of thinking best fits the idea that math is finding patterns?
Check your answer
Notice how the stones grow from section to section, use that rule to figure out longer paths, and check that the answer makes sense
Finding patterns means noticing how things repeat or grow, using that pattern to solve problems and make a general rule, and checking that solutions are reasonable.
Sentence starter
I know ___ because ___.
Goal: I can describe a pattern using the words pattern rule, generalization, and 'each number is ___ more than the one before it.'