Strategy: Add Zero and Subtract Zero – Kindergarten
Big Ideas :
 Add zero: When 0 is added to a quantity, the sum is the same amount
 Subtract zero: When 0 is subtracted from a quantity, the difference is the same amount
 Difference of Zero: When a quantity is subtracted from itself, the difference is zero
 The order of the addends does not change the sum
 Zero means a quantity of nothing
Prerequisite skills:
 One-to-one correspondence
 Cardinality
 Begins to understand that addition is putting together and subtraction is taking away
 Pre-K Curriculum Connections:
o PK.CC.7: Explore relationships by comparing groups of objects up to 10, to determine greater than/more or less than, and equal
to/same (to help build and understanding of zero)
o PK.OA.1 Explore addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out
situations, or verbal explanations.
Curriculum Connections:
 K.OA.1: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g. claps), acting out situations,
verbal explanations, expressions, or equations.
o In addition to other number combinations, be sure to include many examples of adding and subtracting zero and subtracting the
same quantity from itself.
 K.OA.2: Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent
the problem.
o In addition to other number combinations, be sure to include many examples of adding and subtracting zero and subtracting the
same quantity from itself.
 K.NBT.1: Compose and decompose numbers for 11-19 into ten ones and further ones, e.g., by using objects or drawings, and record each
compositions or decomposition by a drawing or equation (such as 18=10+8); understand that these numbers are composed of tens ones
and one, two, three, four, five six, seven, eight, or nine ones.
o Students should use number bonds, part part whole mats, ten frames, math racks, etc to build an understanding of the strategy
of adding and subtracting zero and subtracting the same quantity from itself.
o For fluency purposes, students should be able to state the sum when zero is added and state the difference when zero or the
same quantity is subtracted up to 20. This can be done orally with phrases like
 “If I add nothing to 14 I still have 14”
 “If I take away nothing from 20 I still have 20”
 “If I take 15 from 15 I am left with nothing”
 “6 take away 6 is 0”
 “8 take away 0 is 8”
 “4 plus 0 is 4”
 “I have one ten and four ones, how much do I have if I add zero/take away zero/take away one ten and four ones?”
 “I have one-ten-three. What if I add zero to/take away zero from my total?”
Instructional Strategies:
 Students should understand the idea of the commutative property, but are not expected to use that vocabulary.
 See Mastering the Basic Facts in Addition and Subtraction (O’Connell and SanGiovanni) pages 40-41
 Keep in mind that instruction may be different based on which phase the student exhibits
1. If a student is at the modeling phase and begins counting at zero, your next instructional step would be to have them start at the
larger number in order to understand they don’t need to count on at all.
2. If a student is relying on a number path to count on from zero, the next instructional step would be to wean them from the
number path and recognize it is the same number they should be starting with. They should understand that when you add or
subtract a quantity of nothing, there is no need to move on the number path.
3. If a student is relying on a number path to take away the same quantity (starting at 5 and counting back 5 to zero), the next
instructional step would be to build the understanding of equal amounts and that counting back isn’t necessary when the
quantities are the same. Math Racks make a good model for this because they can take away an entire group of 5 or 10 at one
time.
 Teacher exposes students to number sentences during instruction. Students should be able to write an equation to show their thinking
to match models or pictures. However, students should not be spending time memorizing or solving equations through drill activities
(i.e. flashcards and worksheets).
 Students should be able to show their thinking with an equation, but should also show their thinking using number bonds, part part
whole mats, ten frames, math racks, etc. Using a combination of these tools will build an understanding of the strategy.
 Act out plus zero and subtract zero problems. For example, “7 students were standing in line to get a drink. No more students got in
line. How many students are in line to get a drink?” Ask questions like:
 What does the 7 represent?
 What does the zero represent?
 Why didn’t anyone else get in line to get a drink?
 What does it mean to add zero?
 How did you find the answer?
 Connect adding and subtracting zero to part-part whole. Focusing on boys and girls is a great way to represent part part whole with
adding and subtracting zero. For example, “4 girls were playing soccer at recess. No boys were playing soccer. How many students


were playing soccer?”
Gives students 3 similar problems (5 + 0 = ___, 0 + 2 = ___, 9 + 0 =___ ) and ask questions like:
 What do you notice about the sums?
 What do you notice about the equations?
 Is it easy or hard to add zero? Explain.
This could be done as a whole or small group discussion, an interview, or a journal.
Have students brainstorm scenarios where you might add nothing, take away nothing, or take away the whole amount.
Resources to Support Instruction:
 Commutative Property for Adding Zero
 Number talks (See Number Talks by Sherry Parrish)
o Use ten frames or Math Racks that show amounts only on the top row or bottom row and have a discussion about how mnay
are in each row and how that affects the total.
 Number bonds
o When working with number bonds, be sure to include zero and the quantity as a decomposition of the whole amount.
o See Building Number Sense by Catherine Jones Kuhns for other number bond activities
 Flip cards
o Show students dot flip cards with one side folded back. Then reveal the other side to find a total. Say things like “I see 4, I see 0
more. There are 4 total” or “I see none. I see 4. I see 4 total.” (Use flip cards form Commutative Property Activity above)
o Use part part whole flip cards and reveal only one side. Discuss the addition and subtraction facts it could represent.
 Ten frames
o Have students draw a number card, build that amount on the ten frame, and tell what the total is when adding zero.
o Have students draw a number card, build that amount on the ten frame, and tell what the total is when subtracting zero.
o Have students draw a number card, build that amount on the ten frame, and tell what the total is when subtracting the same
amount.
 Games
o Scoop and Count
o Subtract Zero and All Interactive Game: http://www.mathgames.com/skill/1.72-subtracting-zero-and-all
Assessment:
 Assessments should focus on application of the strategy rather than equations. Asking the following questions may help assess a
student’s understanding of this strategy:
o What is seven and no more?
o What is five take away nothing?

o What is three take away three?
o What is eight plus zero?
o What is four minus zero?
o What is two minus two?
Observation/Interview Recording Tool