Primary & Middle School Mathematics · Grades 1–9
2Addition: First Steps
Three red marbles and two blue marbles: together, how many? Putting together and counting the whole is adding — the first operation, with its two famous signs and .
2.1 Putting together
Definition 2.1 (Addition)
Adding means putting together and counting everything. We write
and read: “three plus two equals five”. The answer of an addition is called the sum.
Example 2.2 (The order does not matter)
and put together the same marbles: both make . To compute , it is faster to start from the bigger number: say “nine”, then count on two — “ten, eleven”. So .
2.2 The ten friends
Example 2.3 (Complements to 10)
Two numbers that make together are “ten friends”:
Ten fingers show them all: raise fingers, and the folded ones are the friend. Knowing the ten friends by heart makes many additions fast.
Method 2.4 (Crossing the ten)
To compute :
- take from the what the needs to reach : that is (its ten friend);
- , and remains from the ;
- . So .
Passing through turns a hard sum into two easy ones.
Example 2.5 (Doubles)
The doubles are worth learning by heart:
Near-doubles come free: is one more than , so .
2.3 Little problems
Example 2.6
“Lea has stickers. She gets more. How many now?” Getting more means adding: (through ten: , then ). Lea has stickers. Always finish with a little sentence!
2.4 Exercises
Exercise 2.1 ★
Draw the marbles and compute: ; ; .
Solution
Solution of Exercise 2.1.
; ; .
Exercise 2.2 ★
Compute by starting from the bigger number: ; ; .
Solution
Solution of Exercise 2.2.
(start at , count on ); ; .
Exercise 2.3 ★
Give the ten friend of: ; ; ; ; .
Solution
Solution of Exercise 2.3.
Ten friends: ; ; ; ; .
Exercise 2.4 ★
Compute through the ten (Method 2.4): ; ; .
Solution
Solution of Exercise 2.4.
(, then ); (, then ); (, then ).
Exercise 2.5 ★
Recite the doubles, then compute using them: ; ; .
Solution
Solution of Exercise 2.5.
(one more than ); (one more than ); (one less than ).
Exercise 2.6 ★
Complete the holes:
Solution
Solution of Exercise 2.6.
; ; .
Exercise 2.7 ★
“In the bus there are children; grown-ups climb in. How many people are in the bus?” Write the addition and the answer sentence.
Solution
Solution of Exercise 2.7.
. There are people in the bus.
Exercise 2.8 ★
Tom has red cars and blue cars. Mia has cars. Who has more cars?
Solution
Solution of Exercise 2.8.
Tom has cars, Mia has : Tom has more.
Exercise 2.9 ★★
Three dice show , and . What is the total? (Add two dice first — choose the two that make a ten friend!)
Solution
Solution of Exercise 2.9.
Add the ten friends and first: , then . The total is .