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Procedural KnowledgeDecompose numbers using standard form (place value) and non-standard form.
Skip count forward and backward by 2, 5, and 10, starting at multiples of 2, 5, and 10 respectively.
Skip count forward by 20 and 25, starting at 0.
Determine the monetary value of collections of coins or bills (cents or dollars) of the same denomination.
Skip count sets, including those with remainders.
Order numbers using benchmarks on a visual or spatial representation.
Represent quantities with numbers.
Relate a numeral to a specific quantity.
Estimate quantities using referents.
Conceptual KnowledgeThe position of a digit in a number determines its value (place value).
Grouping by 10 creates patterns in place value (unitizing) to make working with numbers efficient.
Skip counting is an efficient way of counting larger quantities and can include quantities left over (remainders).
Numbers, including 0, occupy space in a visual or spatial representation of quantity.
Numbers, including 0, can be associated with a specific point on a linear representation of quantity.
The position of something can be indicated using ordinal numbers.
Quantities can be represented symbolically with numerals, including 0.
Estimation is used when an exact count is not needed.
Essential SkillsNumber counting by 2’s, 5’s, 10’s, 20’s and 25’s forward and backward.
Determining ones, tens and hundreds in terms of place value.
Common MisconceptionsDue to the lack of analysis and investigation of a base ten positional system, students might create their own misunderstandings of what this sort of system is about. Students might not realize that:
☆ In a base ten system, we count in groups of ten.
☆ In a base ten system, we only need digits up to 9.
☆ In a positional system, the position of the digit matters.
It is relevant to listen to students’ explanations to address misconceptions.
Big Ideas#1 – The set of whole numbers is infinite, and each whole number can be associated with a unique point on the number line.
#2 – The base ten numeration system is a scheme for recording numbers using digits 0-9, groups of ten, and place value.
#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.
#8 – Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute with mentally.
Key StrategiesExperience counting in different ways, and in different orders.
Represent numbers (concretely, pictorially and symbolically) based on the base ten positional system, and explain the representations.
Connect a digit in a determined position to the number of ones, tens, or hundreds that the digit represents, and explain the connections.
Introduce other numerical systems and compare them to the base ten positional system. Describe and explain differences and similarities.
Key VocabularyBase ten system.
Positional system.
Place value.
One, tens, hundreds.

Grade 2Notion of Halves and Quarters
Procedural KnowledgeCount by halves and quarters to one whole concretely or pictorially.
Partition objects and sets into halves and quarters.
Describe part-to-whole relationships with halves and quarters.
Conceptual KnowledgeObjects and sets can be partitioned into equal-sized parts in different ways.
The part is related to the whole (part-to-whole relationship).
Essential SkillsFinding halves and quarters of sets and objects.
Counting by halves and quarters.
Relating parts to whole.
Common MisconceptionsHalving does not mean splitting into two equal parts, it is just about splitting into two parts. The same misconception is valid for quarters.
There is no need to know what the whole is when working with parts of that whole. Students need to know that a part is always in reference to a whole.
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 halves, quarters, and respective wholes.
Estimate and count by halves and quarters.
Connect concrete, pictorial and symbolic representations of halves, quarters, and respective wholes.
Communicate different strategies for finding halves and quarters of a whole.
Explain strategies for finding halves and quarters of a whole.
Find wholes, given halves or quarters. Explain the process.
Key VocabularuSplit, partition.
Equal parts.
Halves, quarters, whole.
Procedural KnowledgeApply strategies to single-digit addition number facts to a sum of 18 and related subtraction number facts.
Represent addition and subtraction strategies concretely, pictorially, or symbolically.
Add and subtract numbers within 100, including 0, without a calculator.
Recognize patterns in addition and subtraction.
Add and subtract in joining, separating, and comparing situations.
Create and solve problems that involve addition and subtraction.
Conceptual KnowledgeAddition and subtraction are operations used when applying additive thinking strategies.
An addition situation can be represented as a subtraction situation (addition and subtraction are inverse operations).
Addition and subtraction are part-part-whole relationships that can be represented symbolically (+, –, =).
Numbers can be added in any order (commutative and associative properties).
Subtraction strategies.
Addition number facts to 18 and related subtraction number facts.
Common MisconceptionsWhen you add or subtract zero, the result will be zero.
Subtraction is commutative and associative.
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.
#6 – For a given set of numbers there are relationships that are always true, and these are the rules that govern arithmetic and algebra.
#7 – Basic facts and algorithms for operations with whole numbers use notions of equivalence to transform calculations into simpler ones.
Key StrategiesUse concrete, pictorial and symbolic strategies to add and subtract.
Connect concrete, pictorial and symbolic representations of addition and subtraction.
Communicate and explain different strategies for adding and subtracting.
Role play and explain what the commutative and the associative properties mean in addition.
Create and solve problems involving addition and subtraction.
Find, explain and correct errors in problems involving addition and subtraction.
Subtraction, difference.
Commutative property.
Associative property.
Identity element.
Grade 2Sharing and Grouping Using Quantities within 60
Procedural KnowledgeRepresent sharing a set into a given number of groups, with or without remainders.
Represent sharing a set into groups of a given size, with or without remainders.
Group by twos to identify odd and even numbers.
Conceptual KnowledgeSharing and grouping situations can have quantities left over (remainders).
Even quantities can be grouped by 2 with nothing left over.
Odd quantities can be grouped by 2 with 1 left over.
Essential SkillsSharing given the number of groups.
Sharing given the size of groups.
Identifying even and odd numbers.
Common MisconceptionsWhen sharing into a given number of groups, no remainders are expected.
When sharing into groups of a given size, no remainders are expected.
When grouping even numbers, remainders can be expected.
When grouping odd numbers, remainders cannot be expected.
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.
#6 – For a given set of numbers there are relationships that are always true, and these are the rules that govern arithmetic and algebra.
Key StrategiesExperience sharing and grouping in different ways, including with remainders.
Use concrete, pictorial and symbolic strategies to share and group.
Connect concrete, pictorial and symbolic representations of sharing and grouping.
Communicate and explain different strategies for sharing and grouping.
Find, explain and correct errors in sharing and grouping.
Identify even and odd numbers and explain the used strategy.
Key VocabularySharing.
Grouping.
Remainder.
Even and odd numbers.