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Grades 1-2 Math Curriculum Overview - Adapted
from
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Number
Sense and Operations |
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1)
Name and
write (in numerals) whole numbers to 1000, identify the
place values of the digits, and order the numbers. |
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2)
Identify
and distinguish among multiple uses of numbers, including
cardinal (to tell how many) and ordinal (to tell which one
in an ordered list), and numbers as labels and as
measurements. |
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3)
Identify
and represent common fractions (1/2, 1/3, ¼) as parts of
wholes, parts of groups, and numbers on the number line. |
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4)
Compare
whole numbers using terms and symbols (e.g., less than,
equal to, greater than, <, =, >). |
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5)
Identify
odd and even numbers and determine whether a set of
objects has an odd or even number of elements. |
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6)
Identify
the value of all |
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7)
Demonstrate
an understanding of various meanings of addition and
subtraction (e.g., addition as combination—plus,
combined with, more; subtraction as comparison—how much
less, how much more; equalizing—how many more are needed
to make these equal; separation—how much remaining). |
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8)
Understand
and use the inverse relationship between addition and
subtraction (e.g., 8+6=14 is equivalent to 14-6=8 and is
also equivalent to 14-8=6) to solve problems and check
solutions. |
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9)
Know
addition facts (addends to ten) and related subtraction
facts, and use them to solve problems. |
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10)
Demonstrate
the ability to add and subtract three-digit numbers
accurately and efficiently. |
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11)
Demonstrate
in the classroom an understanding of and the ability to
use the conventional algorithms for addition (two 3-digit
numbers and three 2-digit numbers) and subtraction (two
3-digit numbers). |
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12)
Estimate,
calculate, and solve problems involving addition and
subtraction of two-digit numbers. Describe differences
between estimates and actual calculations. |
Patterns,
Relations, and Algebra
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1)
Identify,
reproduce, describe, extend, and create simple rhythmic,
shape, size, number, color, and letter repeating patterns. |
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2)
Identify
different patterns on the hundreds chart. |
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3)
Describe and create addition and subtraction number
patterns (e.g., 1, 4, 7, 10…; or 25, 23, 21…). |
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4)
Skip count by twos, fives, and tens up to at least
50, starting at any number. |
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5)
Construct and solve open sentences that have
variables (e.g.
+7=10). |
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6)
Write number sentences using +, -, <, =, and/or
> to represent mathematical relationships in everyday
situations. |
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7)
Describe functions related to trading, including
coin trades and measurement trades (e.g. five pennies make
one nickel, four cups make one quart, 11 nickels are worth
more than 5 dimes). |
Geometry
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1)
Describe attributes and parts of two-and
three-dimensional shapes (e.g., length of sides, and number
of corners, edges, faces, and sides). |
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2)
Identify, describe, draw, and compare
two-dimensional shapes, including both polygonal (up to six
sides) and curved figures such as circles. |
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3)
Recognize congruent shapes. |
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4)
Identify shapes that have been rotated (turned),
reflected (flipped), translated (slid), and enlarged.
Describe direction of translations (e.g., left, right, up,
down). |
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5)
Identify symmetry in two-dimensional shapes. |
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6)
Predict the results of putting shapes together and
taking them apart. |
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7)
Relate geometric ideas to numbers (e.g., seeing rows
in an array as a model of repeated addition). |
Measurement
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1)
Identify parts of the day (e.g., morning, afternoon,
evening), week, month, and calendar. |
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2)
Tell time at quarter-hour intervals on analog and
digital clocks using a.m. and p.m. |
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3)
Compare the length, weight, area, and volume of two
or more objects by using direct comparison. |
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4)
Measure and compare common objects using metric and
English units of length measurement (e.g. centimeter, inch). |
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5)
Select and correctly use the appropriate measurement
tools (e.g., ruler, balance scale, thermometer). |
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6)
Make and use estimates of measurement, including
time, volume, weight, and area. |
Data
Analysis, Statistics, and Probability
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1)
Use interviews, surveys, and observations to gather
data about themselves and their surroundings |
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2)
Organize, classify, represent, and interpret data
using tallies, charts, tables, bar graphs, pictographs, and
Venn diagrams; interpret the representations. |
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3)
Formulate inferences (draw conclusions) and make
educated guesses (conjectures) about a situation based on
information gained from data. |
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4)
Decide which outcomes of experiments are most
likely. |
Grades 3-4 Math Curriculum Overview - Adapted
from
Fall River
Diocesan Curriculum Guidelines
PLEASE NOTE: These
learner outcomes are presented and/or reinforced over a two-year
period in grades 3 and 4. It
is expected that students (by the end of grade 4) will be able to
do the following:
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Number
Sense and Operations |
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1)
Exhibit an understanding of the base ten number
system by reading, modeling, writing, and interpreting
whole numbers to at least 100,000; demonstrating an
understanding of the values of the digits; and comparing
and ordering the numbers. |
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2)
Represent, order, and compare large numbers (to at
least 100,000) using various forms, including expanded
notation (e.g., 853=8 x 100 + 5 x 10 + 3). |
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3)
Demonstrate an understanding of fractions as parts
of unit wholes, as parts of a collection, and as locations
on the number line. |
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4)
Select, use, and explain models to relate common
fractions and mixed numbers (1/2, 1/3, 1/4, 1/5, 1/6, 1/8,
1/10, 1/12, and 1½), find equivalent fractions, mixed
numbers, and decimals, and order fractions. |
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5)
Identify and generate equivalent forms of common
decimals and fractions less than one whole (halves,
quarters, fifths and tenths). |
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6)
Exhibit an understanding of the base ten number
system by reading, naming, and writing decimals between 0
and 1 up to the hundredths. |
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7)
Recognize classes (in particular, odds, evens;
factors or multiples of a given number; and squares) to
which a number may belong, and identify the numbers in
those classes. Use these in the solution of problems. |
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8)
Select, use, and explain various meanings and
models of multiplication and division of whole numbers.
Understand and use the inverse relationship between the
two operations. |
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9)
Select, use, and explain the commutative,
associative, and identity properties of operations on
whole numbers in problem situations (e.g., 37 x 46 = 46 x
37, (5 x 7) x 2 = 5 x (7 x 2)). |
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10)
Select and use appropriate operations (addition,
subtraction, multiplication, division) to solve problems,
including those involving money. |
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11)
Know multiplication facts through 12 x 12 and
related division facts. Use these facts to solve related
multiplication problems and compute related problems
(e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x
500). |
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12)
Add and subtract (up to five-digit numbers) and
multiply (up to three digits by two digits) accurately and
efficiently. |
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13)
Divide up to a three-digit whole number
with a single-digit divisor (with or without remainders)
accurately and efficiently. |
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14)
Demonstrate in the classroom an
understanding of and the ability to use the conventional
algorithms for addition and subtraction (up to five-digit
numbers), and multiplication (up to three digits by two
digits). |
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15)
Demonstrate in the classroom an
understanding of and the ability to use the conventional
algorithm for division of up to a three-digit whole number
with a single-digit divisor (with or without remainders). |
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16)
Round whole numbers through 100,000 to
the nearest 10, 100, 1000. 10,000, and 100,000. |
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17)
Select and use a variety of strategies
(e.g., front-end, rounding, and regrouping) to estimate
quantities, measures, and the results of whole-number
computations up to three-digit whole numbers and amounts
of money to $1000, and to judge the reasonableness of the
answer. |
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18)
Use concrete objects and visual models
to add and subtract common fractions. |
Patterns,
Relations, and Algebra
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1)
Create, describe, extend and explain symbolic
(geometric) and numeric patterns, including multiplication
patterns like 3, 30,300,3000… |
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2)
Use symbol and letter variables (e.g. Δ. X) to
represent unknowns or quantities that vary in expressions
and in equations or inequalities (mathematical sentences
that use =, <,>). |
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3)
Determine values of variables in simple equations
(e.g. 4106 – Δ =37, 5 = μ + 3). |
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4)
Use pictures, models, tables, charts, graphs, words,
number sentences, and mathematical notations to interpret
mathematical relationships. |
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5)
Solve problems involving proportional relationships,
including unit pricing (e.g., four apples cost 80¢, so one
apple costs 20¢) and map interpretation (e.g. one inch
represents five miles, so two inches represent ten miles). |
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6)
Determine how change in one variable relates to a
change in a second variable (e.g., input-output tables). |
Geometry
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1)
Compare and analyze attributes and other
features (e.g., number of sides, faces, corners, right
angles, diagonals, and symmetry) of two- and
three-dimensional geometric shapes. |
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2)
Describe, model, draw, compare, and
classify two-and three-dimensional shapes (e.g., circles,
polygons—especially triangles and quadrilaterals—cubes,
spheres, and pyramids). |
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3)
Recognize similar figures. |
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4)
Identify angles as acute, right, or
obtuse. |
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5)
Describe and draw intersecting,
parallel, and perpendicular lines. |
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6)
Using ordered pairs of numbers and/or
letters, graph, locate, identify points, and describe paths
(first quadrant). |
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7)
Describe and apply techniques such as
reflections (flips), rotations (turns), and translations
(slides) for determining if two shapes are congruent. |
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8)
Identify and describe line symmetry in
two-dimensional shapes. |
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9)
Predict and validate the results of
partitioning, folding, and combining two- and
three-dimensional shapes. |
Measurement
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1)
Demonstrate an understanding of such
attributes as length, area, weight, and volume, and select
the appropriate type of unit for measuring each attribute. |
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2)
Carry out simple unit conversions within
a system of measurement (e.g., hours to minutes, cents to
dollars, yards to feet or inches, etc.). |
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3) |