Writing Comparisons
3 x 3 = 9
Three times as many as three is nine.
3 times as many as 5 is 15.
3 x 5 = 15
The answer to a multiplication problem.
Product
Abbi has 3 pets. Lily has 3 more pets than Abbi. How many pets does Lily have?
3 + 3 = n; n=6
Philomena has 7 books. Luke has 5 more books than Philomena. How many books does Luke have?
7+5=y;
y=12
7 x 4 = 28
Seven times as many as four is twenty eight
5 times as many as 7 is 35
5 x 7 = 35
The numbers that are being multiplied.
factors
Chassey owns 3 winter coats. Denton owns 5 times as many coats as Chassey. How many winter coats does Denton own?
3x5=n;
n=15
There are 5 horses at the farm. There are 5 times as many cows as there are horses at the farm. How many horses are on the farm?
5 x 5 = y;
y=25
64 = 8 x 8
64 is 8 times as many as 8.
Two ways to show 4 times as many as 3 is 12.
4 x 3 = 12
3 x 4 = 12
Operations that reverse or "undo" each other.
Inverse operation
Brady builds a sandcastle in 15 minutes. Kate builds a sandcastle in 4 fewer minutes than Brady. How long does it take Grace to build a sandcastle?
4 + n = 15;
n=11
Amber reads for 25 minutes every night. Ms. DiBello reads 10 fewer minutes than Amber each night. How many minutes per night does Ms. DiBello spend reading?
10 + y = 25;
y=15
6 x n = 42
Three ways to show 56 is seven times as many as eight.
56 = 7 x 8
56 = 8 x 7
8 x 7 = 56
7 x 8 = 56
Comparing two sets of items to determine how many times as many of any item there is.
Multiplicative Comparison
Emma spends 32 minutes doing her homework. That is 4 times as many minutes as how long Grace spends doing her homework. How much time does Grace spend doing homework?
4 x n = 32;
n=8
Liam and Sara collect different rocks. Liam has collected 45 rocks. That is 5 times as many rocks as Sara collected. How many rocks does Sara have in her collection?
5 x y= 45;
y=9
108 = 12 x n
108 is 12 times as many as 9.
Four ways to show 110 is 11 times as many as ten.
110 = 11 x 10
110 = 10 x 11
10 x 11 = 110
11 x 10 = 110
The two types of comparisons and what key words allow you to know when to use each.
Multiplicative comparison: "times as many"
Additive comparison: "more than"
Emma spends 32 minutes doing her homework. That is 4 times as many minutes as how long Grace spends doing her homework. How many minutes do Grace and Emma spend doing homework altogether?
n = 40 minutes
Liam and Sara collect different rocks. Liam has collected 45 rocks. That is 5 times as many rocks as Sara collected. How many more rocks does Liam collect than Sara?
y = 37 rocks