Patterns
This graph represents one of the two types of patterns we learned about. What kind of pattern is it, what is the initial term, and what is the common difference or ratio?
Arithmetic pattern, Initial term (a): 2, Common difference (d): 2
Mark has 82 coins, which is 3 fewer than 5 times as many as Lisa. How many coins does Lisa?
(Show your work using a diagram and define the variables)
L: The amount of coins that Lisa has
M: The amount of coins that Mark has
Diagrams may vary
Use the number line model to solve: Jane has 8 dolls. She gives away 4 to her sister and then 2 to her friend. How many doll is she left with?
2 dolls.
Use the partial sums method to solve
729+473
Answer is 1202
Change 100five to base 10
25
What would the equation for this chart be?
What is y=81*1/3n-1?
A conference needs to find how many tables they need to fit 185 people.
What is 90 tables?
Show this problem using the set model:
4 apples + 5 apples
9 apples
Use partial differences to solve:
2391-642=
1749
Change 132four to base 10
30
What is the total number of terms in this sequence?
4, 10, 16, 22...214?
What is 36 terms?
Represent this diagram with an equation.
Should be along the lines of G=3M +2 and M+G=138
Explain if subtraction works for these properties. Also include why or why not?
Closure, Commutative, Associate, Additive Identity
Should be something along the lines of:
Closure: Some sets, like integers, work. Whole numbers are not closed under subtraction. It only works with some.
Commutative: No, Associative: No
Additive Identity: Kind of. Depends on the order of the numbers.
Use the chips model to solve:
423five + 34five
1012five
Change 538 to base five
4123five
What is the 24th term in this sequence?
1, 5, 9, 13, 17...
What is 93?
Marty and Carol played mini golf. Their combined score was 104 points. Marty scored 31 less than twice as much as Carol. What were their scores?
(Solve with a diagram)
C=45 M=59
Diagrams may vary
Use the comparison or missing addend model to solve:
John has 6 books. Mary has 13 books. How many more books does John need to have the same amount as Mary?
6 + ___ = 13
6 + 7 =13
Use the partial sums method to solve:
3041five + 214five
2322five
Change 197 to base 4
3011four
59049 is a term in this sequence. What is the position of this term?
3, 9, 27, 81...
What is the 10th term?
Emily has twice as many M&Ms has Tommy. Jonah has 3 times as many as Emily. Jonah has how many times as many M&Ms as Tommy?
(Represent with a diagram. Hint: Substitution!)
Diagrams may vary
Match the example to the correction property: Associative, Additive Identity, Closure, Commutative
When a whole # added to a whole #, the sum of the numbers is still a whole #.
(2+4)+3=(2+3)+4
Number line on board
(9+1)+2=9+(1+2)
A whole # added to whole = closure
(2+4)+3=(2+3)+4 is commutative
Number line is additive identity
(9+1)+2=9+(1+2) is associative property
Use the chips method to solve:
3112four - 232four
131four
Change 3012five to base 10
382