|NMIS PYP Math Scope and Sequence|
|PYP Strand||Grade||Phase 1||Phase 2||Phase 3||Phase 4|
|Math:Numbers||K-5th||Learners will understand that numbers are used for many different purposes in the real world. They will|
develop an understanding of one-to-one correspondence and conservation of number, and be able to
count and use number words and numerals to represent quantities.
|Learners will develop their understanding of the base 10 place value system and will model, read, write,|
estimate, compare and order numbers to hundreds or beyond. They will have automatic recall of addition
and subtraction facts and be able to model addition and subtraction of whole numbers using the
appropriate mathematical language to describe their mental and written strategies. Learners will have
an understanding of fractions as representations of whole-part relationships and will be able to model
fractions and use fraction names in real-life situations.
|Learners will develop the understanding that fractions and decimals are ways of representing whole-part|
relationships and will demonstrate this understanding by modelling equivalent fractions and decimal
fractions to hundredths or beyond. They will be able to model, read, write, compare and order fractions, and
use them in real-life situations. Learners will have automatic recall of addition, subtraction, multiplication
and division facts. They will select, use and describe a range of strategies to solve problems involving
addition, subtraction, multiplication and division, using estimation strategies to check the reasonableness
of their answers.
|Learners will understand that the base 10 place value system extends infinitely in two directions and will|
be able to model, compare, read, write and order numbers to millions or beyond, as well as model integers.
They will develop an understanding of ratios. They will understand that fractions, decimals and percentages
are ways of representing whole-part relationships and will work towards modelling, comparing, reading,
writing, ordering and converting fractions, decimals and percentages. They will use mental and written
strategies to solve problems involving whole numbers, fractions and decimals in real-life situations, using a
range of strategies to evaluate reasonableness of answers.
Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
Understand the relationship between numbers and quantities; connect counting to cardinality.
When counting objects, say the number names in the standard order, pairing each object with one and only one number name and
each number name with one and only one object.
Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of
their arrangement or the order in which they were counted.
Understand that each successive number name refers to a quantity that is one larger.
Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many
as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.
Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group,
e.g., by using matching and counting strategies.1
Compare two numbers between 1 and 10 presented as written numerals.
Operations and Algebraic Thinking
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).
Represent addition and subtraction with objects, fingers, mental images, drawings1, sounds (e.g., claps), acting out situations, verbal explanations,
expressions, or equations.
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer
with a drawing or equation.
Fluently add and subtract within 5.
Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition
or decomposition by a drawing or equation (such as 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four,
five, six, seven, eight, or nine ones.
Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects
with a written numeral.
Understand that the two digits of a two-digit number represent amounts of tens and ones.
10 can be thought of as a bundle of ten ones — called a "ten."
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and
comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent
Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and
equations with a symbol for the unknown number to represent the problem.
Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten
(e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between
addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7
by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the
following equations are true and which are false? 6 = 6, 7 = 8 - 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2.
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown
number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ - 3, 6 + 6 = _.
Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings
and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written
method and explain the reasoning used.
Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models
or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy
to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes
it is necessary to compose a ten.
Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.
Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens,
and 6 ones. Understand the following as special cases:
100 can be thought of as a bundle of ten tens — called a "hundred."
The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens
and 0 ones).
Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition
Add up to four two-digit numbers using strategies based on place value and properties of operations.
Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the
relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit
numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or
decompose tens or hundreds.
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