Kindergarten · Operations · MAT-K-OPS-003
Addition as Putting Together
Model addition by joining two groups within 10.
Learning objectives
What you should be able to do
- Model addition by joining two groups within 10.
- Write or interpret simple addition equations from concrete joining situations.
- Explain the roles of addends, plus sign, equals sign, and sum in age-appropriate language.
Prerequisite check
Make sure the foundation is ready.
Checks part-whole understanding.
Checks ability to determine the joined total.
Learn
Build the idea from meaning, not memorization.
Addition can describe joining
When two separate groups are put together, addition describes the new total. Three red blocks joined with two blue blocks make five blocks altogether.
The equation records the action
The story '3 blocks and 2 more blocks make 5' can be written 3 + 2 = 5. The plus sign means combine the quantities; the equals sign says the expression on the left has the same value as the number on the right.
Count all or count on
Beginners may count every object after joining. As number sense grows, keep the first quantity in mind and count on only the new objects. For 4+2, think 4, then 5,6.
Addition changes the total predictably
If one extra object is added to either addend, the sum becomes one greater. This predictable structure helps learners check whether answers are reasonable.
Interactive math lab
Change it. See what stays true.
Ten-Frame Lab
Fill the frame from left to right and connect the visible amount to the numeral.
5 filled; 5 empty; 10 spaces altogether.
- build two addends
- animate join
- count on
- write equation
Worked examples
Twenty different ways to see the concept work.
Join 1 apple and 1 apple.
1 + 1 = 2Two single objects form a group of two.
Join 2 blocks and 1 block.
2 + 1 = 3Count all three.
Join 1 star and 3 stars.
1 + 3 = 4One joined with three makes four.
Join 2 balls and 2 balls.
2 + 2 = 4Two groups of two make four.
Join 3 counters and 2 counters.
3 + 2 = 5Count 3, then 4,5.
Join 4 counters and 1 counter.
4 + 1 = 5Adding one makes one more.
Join 5 and 0.
5 + 0 = 5Joining an empty group changes nothing.
Join 5 and 1.
5 + 1 = 6One more than five is six.
Join 6 and 2.
6 + 2 = 8Count on 7,8.
Join 7 and 3.
7 + 3 = 10Count on 8,9,10.
A child has 2 crayons and receives 2 more.
2 + 2 = 4The story describes joining.
There are 3 birds and 1 more lands.
3 + 1 = 4The second group joins the first.
A tray has 4 red and 3 blue counters.
4 + 3 = 7All counters form one combined set.
A shelf has 5 books and 2 more are added.
5 + 2 = 7Count on 6,7.
Which equation matches 3 objects joined with 4: 3+4 or 3-4?
3 + 4Joining is represented by addition.
What does the + mean in 2+3?
Combine two quantitiesThe plus sign signals addition.
What does = mean in 2+3=5?
Both sides have the same valueThe left expression equals five.
If 4+2=6, what happens to the sum if one more is added to the second group?
It becomes 7One extra object increases the total by one.
Use counting on for 5+3.
5 → 6 → 7 → 8Three added objects require three forward counts.
Explain why 2+3 and 3+2 have the same total.
Both join the same quantities into five objects.The order of the groups does not change how many objects exist altogether.
Practice
Guided practice with hints
01Model 2+1 with counters.
Hint: Build two, then join one.
Answer: 3
02Model 4+2 by counting on.
Hint: Keep 4 in mind and count two new objects.
Answer: 6
03Which operation describes two groups joining?
Hint: Think about the plus sign.
Answer: Addition
04Complete 3+2=__.
Hint: Count on 4,5.
Answer: 5
05Complete 5+0=__.
Hint: An empty group adds no objects.
Answer: 5
06Tell a joining story for 2+3.
Hint: Start with two things and add three more.
Answer: Any valid story with total 5.
Practice
Independent practice
011+2
Answer: 3
022+2
Answer: 4
033+1
Answer: 4
044+2
Answer: 6
055+3
Answer: 8
066+1
Answer: 7
077+3
Answer: 10
08What operation means joining groups?
Answer: Addition
Common mistakes
Learn to catch the error, not just the answer.
Say the known amount once, then count only the new objects.
Read it as 'has the same value as.'
Ask whether objects are being combined or removed; joining points to addition.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Add the number of red and blue blocks to find how many blocks are present altogether.
- Combine two small groups of snacks and determine the total.
Challenge problems
Create two different joining stories that both represent 4+2.
Any two contexts with four objects joined by two more, totaling six.
Why does 5+0 stay 5?
The second group contains no objects to add.
If 3+4=7, predict 3+5 without recounting all objects.
8, because one extra addend increases the sum by one.
Explain addition using the words parts and whole.
Addition combines parts to determine the whole.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Join the Teams
Combine two small groups and choose the equation and total that match.
Practice
Mastery check
01Model 2+2.
Answer: 4 total
02Solve 4+1.
Answer: 5
03Solve 5+3.
Answer: 8
04Solve 7+3.
Answer: 10
05What does + mean?
Answer: Combine or add quantities.
06What does = mean?
Answer: The two sides have the same value.
07Describe counting on for 4+2.
Answer: Keep 4, then count 5,6.
08Explain why a joining story uses addition.
Answer: Two parts are being combined into one whole.
Terminology
Words to know
- addition
- Combining quantities to find a total.
- addend
- A quantity being added.
- sum
- The total found by addition.
- equals sign
- The symbol = showing that two expressions have the same value.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Kindergarten Operations & Algebraic Thinking
Standards progression for composing, decomposing, adding, and subtracting within 10.