Big Ideas :
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Count on 1: When 1 is added to a quantity, the sum is the next counting number
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Count back 1: When 1 is subtracted from a quantity, the difference is the previous counting number
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The order of the addends does not change the sum
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Students may be at a counting all phase and the goal is to move to counting on from the larger addend or counting back for subtraction.
Prerequisite skills:
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One-to-one correspondence
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Cardinality
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Begins to understand that addition is putting together and subtraction is taking away
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Pre-K Curriculum Connections: o PK.CC.4c: Recognize that each successive number name refers to a quantity that is one larger. 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 o PK.OA.1 Explore addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, or verbal explanations. o PK.OA.2 Decompose quantity (less than or equal to 5, then to 10) into pairs in more than one way (e.g., by using objects or drawings). o PK.OA.3 For any given quantity from (0 to 5, then to 10) find the quantity that must be added to make 5, then to 10, e.g., by using objects or drawings.
Curriculum Connections:
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K.CC.4c: Understand that each successive number name refers to a quantity that is one larger. (0-10) o Although this standard does not specifically address one less, this should be a focus of instruction. o For fluency purposes, students should be able to name one more and one less up to 20. This can be done orally with phrases like “one more than 14 is 15,” “one less than 20 is 19,” “the next number would be ___,” “The number that comes before is
___.”
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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 one more and one less.
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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 one more and one less.

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K.OA.3: Decompose numbers less than or equal to 10 into pairs in more than one way, e.g. by using objects or drawings, and record each decomposition by a drawing or equation (e.g. 5 = 2 + 3 and 5 = 4 + 1) o Students should use number bonds, part part whole mats, ten frames, math racks, etc to build an understanding of the strategy of counting on and counting back one.
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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 counting on and counting back one. o For fluency purposes, students should be able to name one more and one less up to 20. This can be done orally with phrases like
 “one more than 14 is 15”
 “one less than 20 is 19”
 “the next number would be ___”
 “The number that comes before is ___”
 “I have one ten and four ones, what is one more than my total?”
 “I have one-ten-three. What is one less than my total?”
Instructional Strategies:
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Students should understand the idea of the commutative property, but are not expected to use that vocabulary.
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See Mastering the Basic Facts in Addition and Subtraction (O’Connell and SanGiovanni) pages 40-41
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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 with the smaller number your next instructional step would be to have them start at the larger number.
2.
If a student is relying on a number path to count on or back one, the next instructional step would be to wean them from the number path and recognize it is the previous or next number in the counting sequence.
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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).
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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.
Resources to Support Instruction:
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Mouse Count Add One
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Monkeys on a Bed Subtracting One

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Using Number Strips to Visualize One More and One Less
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Commutative Property for Count On One
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Number talks (See Number Talks by Sherry Parrish) o Begin with the number talks on page 73 to build the idea of one more and counting on. o See examples on pages 90-91 that show ten frames with a cluster of dots and one more dot. o See examples on page 83 that use math racks to show a set on top and one on the bottom or one on the top and a set on the bottom.
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Number bonds o Number Bonds Count on One , Count Back One o Number Bonds Practice Count on One, Count Back One o Ladybug Number Bonds o Finding Number Bonds in Pictures o After students have practiced finding number bonds in the picture cards, students can draw their own pictures to show number bonds of plus one o See Building Number Sense by Catherine Jones Kuhns for other number bond activities
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Flip cards o Begin with all dot cards and move to numeral and single dot to encourage counting on from the larger number (use flip cards from commutative property lesson) o Use part part whole flip cards and reveal only one side. Discuss the addition and subtraction facts it could represent. o
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Ten frames o Show students ten frames with a cluster of dots and one more dot in another position to find the total
● ● ●
● ● o Have students draw a number card, build that amount on the ten frame, and add one more to find the total. o Have students draw a number card, build that amount on the ten frame, and take one away to find the total.
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Games o How Many Are Hiding?
o Count on One Bingo o Five in a Row
Assessment:
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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 one more than seven? o What is one less than five? o What is three plus one? o What is five minus one? o What is five take away one?
Observation/Interview Recording Tool