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# Numbers in Grade 1

Grade 1Quantities within 100
Procedural KnowledgeDemonstrate early counting principles, including one-to-one correspondence, stable order, cardinality, conservation of number, hierarchical inclusion, order irrelevance, and abstraction.
Count within 100, forward by 1, starting at any number.
Count backward from 20 to 0 by 1.
Skip count to 100, forward by 5 and 10, starting at 0.
Skip count to 20, forward by 2, starting at 0.
Relate a numeral to a specific quantity.
Represent quantities concretely, including with coins and bills.
Represent quantities pictorially and symbolically.
Recognize the quantity in patterned and non-patterned sets to 10 (conceptual subitizing).
Conceptual KnowledgeThe purpose of counting is to determine how many (quantify).
Quantities can be represented in many ways, including coins and bills.
Quantities can be represented symbolically, including “none” represented by 0.
When counting, a quantity includes all of the previous numbers (hierarchical inclusion).
The count stays the same no matter how the objects are arranged (conservation of number).
Essential SkillsNumber counting by 1’s, forward and backward.
Number counting by 2’s, 5’s and 10’s, forward.
Counting-on.
Counting parts.
Common MisconceptionsCounting needs to be in a specific order.
Partitioning a set into groups and counting using these groups changes the total number in the set.
Big Ideas#3 – Any number can be represented in an infinite number of ways that have the same value.
#4 – Numbers can be compared by their relative values.
Key StrategiesExperience counting in different ways, in different orders and with different objects.
Communicate counting experiences and explain counting approaches.
Pictorially represent a one-to-one correspondence to compare numbers, and explain it.
Represent (concretely and pictorially) one same number in a variety of ways, count to verify the conservation of number, and justify it.
Key VocabularyMore than, fewer than, as many as.
One-to-one correspondence.
Referent.
Counting parts.

Grade 1Notion of One-Half
Split (partition) a set of objects into two equal groups.
Split (partition) an object into two equal-sized pieces.
Conceptual KnowledgeObjects and sets can be split (partitioned) into two equal-sized parts (halves).
Essential SkillsHalving sets and objects.
Common MisconceptionsHalving does not mean splitting into two equal parts, it is just about splitting into two parts.
Big Ideas#3 – Any number can be represented in an infinite number of ways that have the same value.
#4 – Numbers can be compared by their relative values.
#5 – The same number sentence can be associated with different concrete or real-world situations, and different number sentences can be associated with the same concrete or real-world situation.
Key StrategiesUse concrete, pictorial and symbolic examples of halving.
Estimate halves.
Connect concrete, pictorial and symbolic representations of halving.
Communicate different strategies for halving.
Explain halving strategies.
Key VocabularySplit, partition.
Equal parts, halves.
Grade 1Sharing and Grouping Using Quantities Within 20
Procedural KnowledgeExplore equal-sharing and equal-grouping situations concretely or pictorially.
Represent equal-sharing and equal-grouping situations concretely or pictorially.
Apply conservation of number when sharing or grouping.
Conceptual KnowledgeSome quantities can be shared or grouped equally.
The quantity stays the same no matter how the objects are grouped or shared (conservation of number).
Essential SkillsEqual-sharing and equal-grouping.
Common MisconceptionsEqual-sharing does not mean splitting into equal parts, it is just about splitting into parts.
Equal-grouping does not necessarily refer to having equal groups, it is just about having groups.
(Part of these misconceptions may be due to the use of the words “sharing” and “grouping”, instead of “equal-sharing” and “equal-grouping”.)
Big Ideas#3 – Any number can be represented in an infinite number of ways that have the same value.
#4 – Numbers can be compared by their relative values.
#5 – The same number sentence can be associated with different concrete or real-world situations, and different number sentences can be associated with the same concrete or real-world situation.
Key StrategiesUse concrete, pictorial and symbolic strategies to equal-share and equal-group.
Connect concrete, pictorial and symbolic representations of equal-sharing and equal-grouping.
Communicate different strategies for equal-sharing and equal-grouping
Explain strategies for equal-sharing and equal-grouping.
Find, explain and correct errors in equal-sharing and equal-grouping.
Key VocabularyEqual-sharing.
Equal-grouping.
Equal-grouping does not necessarily refer to having equal groups, it is just about having groups.
Grade 1Composition and Decomposition of Quantities
Procedural KnowledgeExplore various ways to compose and decompose quantities.
Explore patterns in addition and subtraction.
Represent addition and subtraction strategies concretely, pictorially, or symbolically.
Add and subtract in joining, separating, and comparing situations.
Add and subtract quantities within 20, including 0, without a calculator.
Recall single-digit addition number facts to a sum of 10 and related subtraction number facts.
Conceptual KnowledgeAddition and subtraction are operations used to compose and decompose numbers.
Part-part-whole relationships can be represented using addition and subtraction.
Two numbers can be added in any order (commutative property).
Essential SkillsAddition number facts to 10 and related subtraction number facts.
Common MisconceptionsIf you add one in an addition, for example from 6 + 9 to 6 + 10, then you need to add one to the final sum to compensate.
If you subtract one from an addition, for example from 6 + 7 to 6 + 6, then you need to subtract one to the final sum to compensate.
Big Ideas#3 – Any number or numerical expression can be represented in an infinite number of ways that have the same value.
#5 – The same number sentence can be associated with different concrete or real-world situations, and different number sentences can be associated with the same concrete or real-world situation.
#7 – Basic facts for operations with whole numbers use notions of equivalence to transform calculations into simpler ones.
Key StrategiesUse concrete, pictorial and symbolic strategies to compose and decompose quantities.
Use concrete, pictorial and symbolic strategies to add and subtract.
Connect concrete, pictorial and symbolic representations of composition and decomposition.
Connect concrete, pictorial and symbolic representations of addition and subtraction.
Communicate different strategies for composing and decomposing.
Communicate different strategies for adding and subtracting.
Explain addition and subtraction strategies.
Find, explain and correct errors in composing and decomposing.
Find, explain and correct errors in addition and subtraction.
Key VocabularyComposition, decomposition.