Ohio
Academic Content Standards for Mathematics
Grades K-5
Kindergarten Click
here for kindergarten Investigations units
Number,
Number Sense, and Operations
N1. Compare and order whole numbers up to
10.
N2. Explain rules of counting, such as each
object should be counted once and that order does not change the number.
N3. Count to twenty; e.g., in play
situations or while reading number books.
N4. Determine how many in sets (groups) of
10 or fewer objects.
N5. Relate, read and write numerals for
single-digit numbers (0 to 9).
N6. Construct multiple sets of objects each
containing the same number of objects.
N7. Compare the number of objects in two or
more sets when one set has one or two more, or one or two fewer objects.
N8. Represent and use whole numbers in
flexible ways, including relating, composing and decomposing numbers; e.g., 5 marbles
can be 2 red and 3 green or 1 red and 4 green.
N9. Identify and state the value of a
penny, nickel and dime.
N10a. Model and represent addition as
combining sets and counting on, and subtraction as take-away and comparison.
For example: combine and separate small sets of objects in contextual
situations; e.g., add or subtract one, two, or another small amount.
N10b. Model and
represent addition as combining sets and counting on, and subtraction as
take-away and comparison. For example: count on (forward) and count back
(backward) on a number line between 0 and 10.
N11. Demonstrate joining multiple groups of
objects, each containing the same number of objects; e.g., combining 3 bags of
candy, each containing 2 pieces.
N12. Partition or share a small set of
objects into groups of equal size; e.g., sharing 6 stickers equally among 3
children.
N13. Recognize the number or quantity of
sets up to 5 without counting; e.g., recognize without counting the dot
arrangement on a domino as 5.
Measurement
M1. Identify units of time (day, week,
month, year) and compare calendar elements; e.g., weeks are longer than days.
M2. Compare and order objects of different
lengths, areas, weights and capacities; and use relative terms, such as longer,
shorter, bigger, smaller, heavier, lighter, more and less.
M3a. Measure length and volume (capacity)
using uniform objects in the environment. For example, find how many paper
clips long is a pencil.
M3b. Measure length and volume (capacity)
using uniform objects in the environment. For example, find how many small
containers it takes to fill one big container using sand, rice, beans.
M4a. Order events based on time. For
example, activities that take a long or short time.
M4b. Order events based on time. For example,
review what we do first, next, last.
M4c. Order events based on time. For
example, recall what we did or plan to do yesterday, today, tomorrow.
Geometry
and Spatial Sense
G1a. Identify and sort two-dimensional
shapes and three-dimensional objects. For example, identify and describe
two-dimensional figures and three-dimensional objects from the environment
using the childs own vocabulary.
G1b. Identify and sort two-dimensional
shapes and three-dimensional objects. For example, sort shapes and objects into
groups based on student-defined categories.
G1c. Identify and sort two-dimensional
shapes and three-dimensional objects. For example, select all shapes or objects
of one type from a group.
G1d. Identify and sort two-dimensional
shapes and three-dimensional objects. For example: build two-dimensional
figures using paper shapes or tangrams; build simple three-dimensional objects
using blocks.
G2a. Name and demonstrate the relative
position of objects as follows: place objects over, under, inside, outside, on,
beside, between, above, below, on top of, upside-down, behind, in back of, in
front of.
G2b. Name and demonstrate the relative
position of objects as follows: describe placement of objects with terms, such
as on, inside, outside, above, below, over, under, beside, between, in front
of, behind.
Patterns,
Functions, and Algebra
A1a. Sort, classify and order objects by
size, number and other properties.
For example, identify how objects are alike and different.
A1b. Sort, classify and order objects by
size, number and other properties.
For example: order three events or objects according to a given
attribute, such as time or size.
A1c. Sort, classify and order objects by
size, number and other properties.
For example, recognize and explain how objects can be classified in more
than one way.
A1d. Sort, classify and order objects by
size, number and other properties.
For example, identify what attribute was used to sort groups of objects
that have already been sorted.
A2. Identify, create, extend and copy
sequences of sounds (such as musical notes), shapes (such as buttons, leaves or
blocks), motions (such as hops or skips), and numbers from 1 to 10.
A3. Describe orally the pattern of a given
sequence.
A4. Model a problem situation using
physical materials.
Data
Analysis and Probability
D1. Gather and sort data in response to
questions posed by teacher and students; e.g., how many sisters and brothers,
what color shoes.
D2. Arrange objects in a floor or table
graph according to attributes, such as use, size, color or shape.
D3. Select the category or categories that
have the most or fewest objects in a floor or table graph.
Grade 1 Click
here for first grade Investigations
units
Number,
Number Sense, and Operations
N1. Use ordinal numbers to order objects;
e.g., first, second, third.
N2. Recognize and generate equivalent forms
for the same number using physical models, words and number expressions; e.g.,
concept of ten is described by 10 blocks, full tens frame, numeral 10, 5 + 5,
15 - 5, one less than 11, the age of my brother.
N3. Read and write the numerals for numbers
to 100.
N4. Count forward to 100, count backwards
from 100, and count or backward starting at any number between 1 and 100.
N5a. Develop a system to group and count by
twos, fives and tens.
N5b. Identify patterns and groupings in a
100s chart and relate to place value concepts.
N5c. Recognize the first digit of a two-digit
number as the most important to indicate size of a number and the nearness to
10 or 100.
N6. Identify and state the value of a
penny, nickel, dime, quarter and dollar.
N7. Determine the value of a small
collection of coins (with a total value up to one dollar) using 1 or 2
different type coins, including pennies, nickels, dimes and quarters.
N8. Show different combinations of coins
that have the same value.
N9. Represent commonly used fractions using
words and physical models for halves, thirds and fourths, recognizing fractions
are represented by equal size parts of a whole and of a set of objects.
N10a. Model and explain addition using
physical materials in contextual situations.
N10b. Draw pictures to model addition.
N10c. Write number sentences to represent
addition.
N10d. Explain that adding two whole numbers
yields a larger whole number.
N11a. Model and explain subtraction using
physical materials in contextual situations.
N11b. Draw pictures to model subtraction.
N11c. Write number sentences to represent
subtraction.
N11d. Explain that subtraction of whole
numbers yields an answer smaller than the original number.
N12. Use conventional symbols to represent
the operations of addition and subtraction.
N13.
Model and represent multiplication
as repeated addition and rectangular arrays in contextual situations; e.g.,
four people will be at my party and if I want to give 3 balloons to each
person, how many balloons will I need to buy?
N14. Model and represent division as sharing
equally in contextual situations; e.g., sharing cookies.
N15. Demonstrate that equal means the
same as
using visual representations.
N16a. Develop strategies for basic addition
facts, such as counting all.
N16b. Develop strategies for basic addition
facts, such as counting on.
N16c. Develop strategies for basic addition
facts, such as one more, two more.
N16d. Develop strategies for basic addition
facts, such as doubles.
N16e. Develop strategies for basic addition
facts, such as doubles plus or minus one.
N16f. Develop strategies for basic addition
facts, such as making ten.
N16g. Develop strategies for basic addition
facts, such as using tens frames.
N16h. Develop strategies for basic addition
facts, such as: identity property (adding zero).
N17a. Develop strategies for basic
subtraction facts, such as relating to addition (for example, think of 7 - 3 =
? as 3 plus ? equals 7).
N17b. Develop strategies for basic
subtraction facts, such as one less, two less.
N17c. Develop strategies for basic
subtraction facts, such as all but one (for example, 8 - 7, 5 - 4).
N17d. Develop strategies for basic
subtraction facts, such as: using tens frames.
N17e. Develop strategies for basic
subtraction facts, such as missing addends.
Measurement
M1. Recognize and explain the need for
fixed units and tools for measuring length and weight; e.g., rulers and balance
scales.
M2. Tell time to the hour and half hour on
digital and analog (dial) timepieces.
M3. Order a sequence of events with respect
to time; e.g., summer, fall, winter and spring; morning, afternoon and night.
M4. Estimate and measure weight using
non-standard units; e.g., blocks of uniform size.
M5. Estimate and measure lengths using
non-standard and standard units; i.e., centimeters, inches and feet.
Geometry
and Spatial Sense
G1a. Recognize and identify triangles and
rhombuses independent of position, shape or size.
G1b. Describe two-dimensional shapes using attributes
such as number of sides and number of vertices (corners or angles).
G2. Create new shapes by combining or
cutting apart existing shapes.
G3. Identify the shapes of the faces of
three-dimensional objects.
G4. Extend the use of location words to
include distance (near, far, close to) and directional words (left, right).
G5. Copy figures and draw simple
two-dimensional shapes from memory.
Patterns,
Functions, and Algebra
A1. Sort, classify and order objects by two
or more attributes, such as color and shape, and explain how objects were
sorted.
A2a. Analyze and describe patterns with
multiple attributes using numbers and shapes; e.g., AA, B, aa, b, AA, B, aa,
b,
A2b. Continue repeating and growing patterns
with materials, pictures and geometric items; e.g., XO, XOO, XOOO, XOOOO.
A3. Describe orally the basic unit or
general plan of a repeating or growing pattern.
A4. Solve open sentences by representing an
expression in more than one way using the commutative property; e.g., 4 + 5 = 5
+ 4 or the number of blue balls plus red balls is the same as the number of red
balls plus blue balls (R + B = B +
R).
A5. Describe orally and model a problem
situation using words, objects or number phrase or sentence.
Data
Analysis and Probability
D1. Identify multiple categories for
sorting data.
D2. Collect and organize data into charts
using tally marks.
D3. Display data in picture graphs with
units of 1 and bar graphs with intervals of 1.
D4. Read and interpret charts, picture
graphs and bar graphs as sources of information to identify main ideas, draw
conclusions, and make predictions.
D5. Construct a question that can be
answered by using information from a graph.
D6. Arrange five objects by an attribute,
such as size or weight, and identify the ordinal position of each object.
D7. Answer questions about the number of
objects represented in a picture graph, bar graph or table graph; e.g.,
category with most, how many more in a category compared to another, how many
altogether in two categories.
D8. Describe the likelihood of simple
events as possible/impossible and more likely/less likely; e.g., when using
spinners or number cubes in classroom activities.
Grade 2 Click
here for second grade Investigations units
Number,
Number Sense, and Operations
N1a. Use place value concepts to represent,
compare and order whole numbers using physical models, numerals and words, with
ones, tens and hundreds; recognize 10 can mean 10 ones or one entity (1 ten)
through physical models and trading games.
N1b. Use place value concepts to represent,
compare and order whole numbers using physical models, numerals and words, with
ones, tens and hundreds: read and write 3-digit numerals (e.g., 243 in words,
24 tens and 3 ones, etc.) and construct models.
N2. Recognize and classify numbers as even
or odd.
N3. Count money and make change using coins
and a dollar bill.
N4. Represent and write the value of money using
the sign and in decimal form when using the $ sign.
N5a. Represent fractions (halves, thirds,
fourths, sixths and eighths), using words, numerals and physical models. For
example, recognize that a fractional part can mean different amounts depending
on the original quantity.
N5b. Represent fractions (halves, thirds,
fourths, sixths and eighths), using words, numerals and physical models. For
example, recognize that a fractional part of a rectangle does not have to be
shaded with contiguous parts.
N5c. Represent fractions (halves, thirds,
fourths, sixths and eighths), using words, numerals and physical models. For
example, identify and illustrate parts of a whole and parts of sets of objects.
N5d. Represent fractions (halves, thirds,
fourths, sixths and eighths), using words, numerals and physical models. For
example, compare and order physical models of halves, thirds and fourths in
relation to 0 and 1.
N6. Model, represent and explain
subtraction as comparison, take-away and part-to-whole; e.g., solve missing addend problems by
counting up or subtracting.
N7. Model, represent and explain
multiplication as repeated addition, rectangular arrays and skip counting.
N8. Model, represent and explain division
as sharing equally and repeated subtraction.
N9. Model and use the commutative property
for addition.
N10. Demonstrate fluency in addition facts
with addends through 9 and corresponding subtractions; e.g., 9 + 9 = 18, 18
– 9 = 9.
N11. Add and subtract multiples of 10.
N12a. Demonstrate multiple strategies for
adding and subtracting 2- or 3-digit whole numbers, such as compatible numbers.
N12b. Demonstrate multiple strategies for
adding and subtracting 2- or 3-digit whole numbers, such as compensatory
numbers.
N12c. Demonstrate multiple strategies for
adding and subtracting 2- or 3-digit whole numbers, such as informal use of
commutative and associative properties of addition.
N13. Estimate the results of whole number
addition and subtraction problems using front-end estimation, and judge the
reasonableness of the answers.
Measurement
M1a. Identify and select appropriate units
of measure for length – centimeters, meters, inches, feet or yards.
M1b. Identify and select appropriate units
of measure for volume (capacity) – liters, cups, pints or quarts.
M1c. Identify and select appropriate units
of measure for weight – grams, ounces or pounds.
M1d. Identify and select appropriate units
of measure for time – hours, half-hours, quarter-hours or minutes and
time designations, a.m. or p.m.
M2. Establish personal or common referents
for units of measure to make estimates and comparisons; e.g., the width of a
finger is a centimeter, a large bottle of soda pop is 2 liters, a small paper
clip weighs about one gram.
M3. Describe and compare the relationships
among units of measure, such as centimeters and meters; inches, feet and yards;
cups, pints and quarts; ounces and pounds; and hours, half-hours, and
quarter-hours; e.g., how many inches in a foot?
M4. Tell time to the nearest minute interval
on digital and to the nearest 5-minute interval on analog (dial) timepieces.
M5. Estimate and measure the length and
weight of common objects, using metric and U.S. customary units, accurate to
the nearest unit.
M6. Select and use appropriate measurement
tools; e.g., a ruler to draw a segment 3 inches long, a measuring cup to place
2 cups of rice in a bowl, a scale to weigh 50 grams of candy.
M7. Make and test predictions about
measurements, using different units to measure the same length or volume.
Geometry
and Spatial Sense
G1. Identify, describe, compare and sort
three-dimensional objects (i.e., cubes, spheres, prisms, cones, cylinders and
pyramids) according to the shape of the faces or the number of faces, edges or
vertices.
G2. Predict what new shapes will be formed
by combining or cutting apart existing shapes.
G3. Recognize two-dimensional shapes and
three-dimensional objects from different positions.
G4. Identify and determine whether
two-dimensional shapes are congruent (same shape and size) or similar (same
shape different size) by copying or using superposition (lay one thing on top
of another).
G5. Create and identify two-dimensional
figures with line symmetry; e.g., what letter shapes, logos, polygons are
symmetrical?
Patterns,
Functions, and Algebra
A1. Extend simple number patterns (both
repeating and growing patterns), and create similar patterns using different
objects, such as using physical materials or shapes to represent numerical
patterns.
A2. Use patterns to make generalizations
and predictions; e.g., determine a missing element in a pattern.
A3. Create new patterns with consistent
rules or plans, and describe the rule or general plan of existing patterns.
A4. Use objects, pictures, numbers and
other symbols to represent a problem situation.
A5. Understand equivalence and extend the
concept to situations involving symbols; e.g., 4 + 5 = 9 and 9 = 4 + 5, and 4 +
5 = 3 + 6 = + □
A6. Use symbols to represent unknown
quantities and identify values for symbols in an expression or equation using
addition and subtraction; e.g., □ + О = 10, - 2 = 4.
A7. Describe qualitative and quantitative
changes, especially those involving addition and subtraction; e.g., a student
growing taller versus a student growing two inches in one year.
Data
Analysis and Probability
D1. Pose questions, use observations,
interviews and surveys to collect data, and organize data in charts, picture
graphs and bar graphs.
D2. Read, interpret and make comparisons
and predictions from data represented in charts, line plots, picture graphs and
bar graphs.
D3. Read and construct simple timelines to
sequence events.
D4. Write a few sentences to describe and
compare categories of data represented in a chart or graph, and make statements
about the data as a whole.
D5. Identify untrue or inappropriate
statements about a given set of data.
D6. Recognize that data may vary from one
population to another; e.g., favorite TV shows of students and of parents.
D7. List some of the possible outcomes of a
simple experiment, and predict whether given outcomes are more, less or equally
likely to occur.
D8. Use physical models and pictures to
represent possible arrangements of 2 or 3 objects.
Grade 3 Click
here for third grade Investigations
units
Number,
Number Sense, and Operations
N1. Identify and generate equivalent forms
of whole numbers; e.g., 36, 30 + 6, 9 x 4, 46 - 10, number of inches in a
yard.
N2a. Recognize 100 means 10 tens as well as
a single entity (1 hundred) through physical models and trading games.
N2b. Describe the multiplicative nature of
the number system; e.g., the structure of 3205 as 3 x 1000 plus 2 x 100 plus 5
x 1.
N2c. Model the size of 1000 in multiple
ways; e.g., packaging 1000 objects into 10 boxes of 100, modeling a meter with
centimeter and decimeter strips, or gathering 1000 pop-can tabs.
N2d. Explain the concept of tenths and
hundredths using physical models, such as metric pieces, base ten blocks,
decimal squares or money.
N3. Use mathematical language and symbols
to compare and order; e.g., less than, greater than, at most, at least,
(symbols).
N4. Count money and make change using coins
and paper bills to ten dollars.
N5. Represent fractions and mixed numbers
using words, numerals and physical models.
N6. Compare and order commonly used
fractions and mixed numbers using number lines, models (such as fraction
circles or bars), points of reference (such as more or less than ½), and
equivalent forms using physical or visual models.
N7. Recognize and use decimal and fraction
concepts and notations as related ways of representing parts of a whole or a
set; e.g., 3 of 10 marbles are red can also be described as 3/10 and 3 tenths
are red.
N8a. Model, represent and explain
multiplication; e.g., repeated addition, skip counting, rectangular arrays and
area model. For example, use conventional mathematical symbols to write
equations for word problems involving multiplication.
N8b. Model, represent and explain
multiplication; e.g., repeated addition, skip counting, rectangular arrays and
area model; understand that, unlike addition/subtraction, the factors in
multiplication and division may have different units; e.g., 3 boxes of 5
cookies.
N9a. Model, represent and explain division;
e.g., sharing equally, repeated subtraction, rectangular arrays and area model.
For example, translate contextual situations involving division into
conventional mathematical symbols.
N9b. Model, represent and explain division;
e.g., sharing equally, repeated subtraction, rectangular arrays and area model.
For example, explain how a remainder may impact an answer in a real-world
situation; e.g., 14 cookies being shared by 4 children.
N10a. Relate addition and subtraction as
inverse operations.
N10b. Relate multiplication and division as
inverse operations.
N10c. Relate addition to multiplication
(repeated addition).
N10d. Relate subtraction to division
(repeated subtraction).
N11. Model and use the commutative and
associative properties for addition and multiplication.
N12. Add and subtract whole numbers with and
without regrouping.
N13. Demonstrate fluency in multiplication
facts through 10 and corresponding division facts.
N14. Multiply and divide 2- and 3-digit
numbers by a single-digit number, without remainders for division.
N15. Evaluate the reasonableness of
computations based upon operations and the numbers involved; e.g., considering
relative size, place value and estimates.
Measurement
M1a. Identify and select appropriate units
for measuring length – miles, kilometers and other units of measure as
appropriate.
M1b. Identify and select appropriate units
for measuring volume (capacity) – gallons.
M1c. Identify and select appropriate units
for measuring weight – ounces, pounds, grams, or kilograms.
M1d. Identify and select appropriate units
for measuring temperature – degrees (Fahrenheit or Celsius).
M2. Establish personal or common referents
to include additional units; e.g., a gallon container of milk; a postage stamp
is about a square inch.
M3. Tell time to the nearest minute and
find elapsed time using a calendar or a clock.
M4. Read thermometers in both Fahrenheit
and Celsius scales.
M5. Estimate and measure length, weight and
volume (capacity), using metric and U.S. customary units, accurate to the
nearest 1/2 or 1/4 unit as appropriate.
M6. Use appropriate measurement tools and
techniques to construct a figure or approximate an amount of specified length,
weight or volume (capacity).
M7. Make estimates for perimeter, area and
volume using links, tiles, cubes and other models.
Geometry
and Spatial Sense
G1. Analyze and describe properties of
two-dimensional shapes and three-dimensional objects using terms such as
vertex, edge, angle, side and face.
G2a. Use physical models, like straws, to
make different sized angles by opening and closing the sides, not by changing
the side lengths.
G2b. Identify, classify and draw right,
acute, obtuse and straight angles.
G3. Find and name locations on a labeled
grid or coordinate system; e.g., a map or graph.
G4. Draw lines of symmetry to verify
symmetrical two-dimensional shapes.
G5. Build a three-dimensional model of an
object composed of cubes; e.g., construct a model based on an illustration or
actual object.
Patterns,
Functions, and Algebra
A1. Extend multiplicative and growing
patterns, and describe the pattern or rule in words.
A2. Analyze and replicate arithmetic
sequences with and without a calculator.
A3. Use patterns to make predictions,
identify relationships, and solve problems.
A4. Model problem situations using objects,
pictures, tables, numbers, letters and other symbols.
A5. Write, solve and explain simple
mathematical statements, such as 7 + □ > 8 or + 8 =
10.
A6. Express mathematical relationships as
equations and inequalities.
A7. Create tables to record, organize and
analyze data to discover patterns and rules.
A8. Identify and describe quantitative
changes, especially those involving addition and subtraction; e.g., the height
of water in a glass becoming 1 centimeter lower each week due to evaporation.
Data
Analysis and Probability
D1. Collect and organize data from an
experiment, such as recording and classifying observations or measurements, in
response to a question posed.
D2. Draw and interpret picture graphs in
which a symbol or picture represents more than one object.
D3. Read, interpret and construct bar
graphs with intervals greater than one.
D4. Support a conclusion or prediction
orally and in writing, using information in a table or graph.
D5. Match a set of data with a graphical
representation of the data.
D6. Translate information freely among
charts, tables, line plots, picture graphs and bar graphs; e.g., create a bar
graph from the information in a chart.
D7. Analyze and interpret information
represented on a timeline.
D8. Identify the mode of a data set and
describe the information it gives about a data set.
D9. Conduct a simple experiment or
simulation of a simple event, record the results in a chart, table or graph,
and use the results to draw conclusions about the likelihood of possible
outcomes.
D10.
Use physical models, pictures,
diagrams and lists to solve problems involving possible arrangements or
combinations of two to four objects.
Grade 4 Click
here for fourth grade Investigations units
Number,
Number Sense, and Operations
N1a. Connect physical, verbal and symbolic
representations of fractions, decimals and whole numbers; e.g., 1/2, 5/10, five
tenths, 0.5, and shaded rectangles with half.
N1b. Understand and explain that ten tenths
is the same as one whole in both fraction and decimal form.
N2. Use place value structure of the
base-ten number system to read, write, represent and compare whole numbers
through millions and decimals through thousandths.
N3. Round whole numbers to a given place
value.
N4. Identify and represent factors and
multiples of whole numbers through 100, and classify numbers as prime or
composite.
N5. Use models and points of reference to
compare commonly used fractions.
N6. Use associative and distributive
properties to simplify and perform computations; e.g., use left to right
multiplication and the distributive property to find an exact answer without
paper and pencil, such as 5 x 47 = 5 x 40 + 5 x 7 = 200 + 35 = 235.
N7. Recognize that division may be used to
solve different types of problem situations and interpret the meaning of
remainders; e.g., situations involving measurement, money.
N8. Solve problems involving counting money
and making change, using both coins and paper bills.
N9. Estimate the results of computations
involving whole numbers, fractions and decimals, using a variety of strategies.
N10. Use physical models, visual
representations, and paper and pencil to add and subtract decimals and commonly
used fractions with like denominators.
Measurement
M1. Relate the number of units to the size
of the units used to measure an object; e.g., compare the number of cups to
fill a pitcher to the number of quarts to fill the same pitcher.
M2. Demonstrate and describe perimeter as
surrounding and area as covering a two-dimensional shape, and volume as filling
a three-dimensional object.
M3a. Identify and select appropriate units
to measure perimeter – string or links (inches or centimeters).
M3b. Identify and select appropriate units
to measure area – tiles (square inches or square centimeters).
M3c. Identify and select appropriate units
to measure volume – cubes (cubic inches or cubic centimeters).
M4. Develop and use strategies to find
perimeter using string or links, area using tiles or a grid, and volume using
cubes; e.g., count squares to find area of regular or irregular shapes on a
grid, layer cubes in a box to find its volume.
M5. Make simple unit conversions within a
measurement system; e.g., inches to feet, kilograms to grams, quarts to
gallons.
M6. Write, solve and verify solutions to
multi-step problems involving measurement.
Geometry
and Spatial Sense
G1. Identify, describe and model
intersecting, parallel and perpendicular lines and line segments; e.g., use straws
or other material to model lines.
G2. Describe, classify, compare and model
two- and three-dimensional objects using their attributes.
G3. Identify similarities and differences
of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids.
G4. Identify and define triangles based on
angle measures (equiangular, right, acute and obtuse triangles) and side
lengths (isosceles, equilateral and scalene triangles).
G5. Describe points, lines and planes, and
identify models in the environment.
G6. Specify locations and plot ordered
pairs on a coordinate plane, using first quadrant points.
G7. Identify, describe and use reflections
(flips), rotations (turns), and translations (slides) in solving geometric
problems; e.g., use transformations to determine if 2 shapes are congruent.
G8. Use geometric models to solve problems
in other areas of mathematics, such as number (multiplication/division) and
measurement (area, perimeter, border).
Patterns,
Functions, and Algebra
A1. Use models and words to describe,
extend and make generalizations of patterns and relationships occurring in
computation, numerical patterns, geometry, graphs and other applications.
A2. Represent and analyze patterns and
functions using words, tables and graphs.
A3. Construct a table of values to solve
problems associated with a mathematical relationship.
A4. Use rules and variables to describe
patterns and other relationships.
A5. Represent mathematical relationships
with equations or inequalities.
A6. Describe how a change in one variable
affects the value of a related variable; e.g., as one increases the other
increases or as one increases the other decreases.
Data
Analysis and Probability
D1. Create a plan for collecting data for a
specific purpose.
D2. Represent and interpret data using
tables, bar graphs, line plots and line graphs.
D3. Interpret and construct Venn diagrams
to sort and describe data.
D4. Compare different representations of
the same data to evaluate how well each representation shows important aspects
of the data, and identify appropriate ways to display the data.
D5. Propose and explain interpretations and
predictions based on data displayed in tables, charts and graphs.
D6. Describe the characteristics of a set
of data based on a graphical representation, such as range of the data, clumps
of data, and holes in the data.
D7. Identify the median of a set of data
and describe what it indicates about the data.
D8. Use range, median and mode to make
comparisons among related sets of data.
D9. Conduct simple probability experiments
and draw conclusions from the results; e.g., rolling number cubes or drawing
marbles from a bag.
D10. Represent the likelihood of possible
outcomes for chance situations; e.g., probability of selecting a red marble
from a bag containing 3 red and 5 white marbles.
D11. Relate the concepts of impossible and
certain-to-happen events to the numerical values of 0 (impossible) and 1
(certain).
D12. Place events in order of likelihood and
use a diagram or appropriate language to compare the chance of each event
occurring; e.g., impossible, unlikely, equal, likely, certain.
D13. List and count all possible
combinations using one member from each of several sets, each containing 2 or 3
members; e.g., the number of possible outfits from 3 shirts, 2 shorts and 2
pairs of shoes.
Grade 5 Click
here for fifth grade Investigations
units
Number,
Number Sense, and Operations
N1. Use models and visual representation to
develop the concept of ratio as part-to-part and part-to-whole, and the concept
of percent as part-to-whole.
N2. Use various forms of 1 to demonstrate
the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = ¾ x 6/6.
N3. Identify and generate equivalent forms
of fractions, decimals and percents.
N4.
Round decimals to a given place value and round fractions (including
mixed numbers) to the nearest half.
N5. Recognize and identify perfect squares
and their roots.
N6. Represent and compare numbers less than
0 by extending the number line and using familiar applications; e.g.,
temperature, owing money.
N7.
Use commutative, associative, distributive, identity and inverse
properties to simplify and perform computations.
N8. Identify and use relationships between
operations to solve problems.
N9. Use order of operations, including use
of parentheses, to simplify numerical expressions.
N10. Justify why fractions need common
denominators to be added or subtracted.
N11.
Explain how place value is related to addition and subtraction of
decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because
they are both tenths.
N12. Use physical models, points of
reference, and equivalent forms to add and subtract commonly used fractions
with like and unlike denominators and decimals.
N13. Estimate the results of computations
involving whole numbers, fractions and decimals, using a variety of strategies.
Measurement
M1. Identify and select appropriate units to
measure angles; i.e., degrees.
M2. Identify paths between points on a grid
or coordinate plane and compare the lengths of the paths; e.g., shortest path,
paths of equal length.
M3. Demonstrate and describe the
differences between covering the faces (surface area) and filling the interior
(volume) of three-dimensional objects.
M4. Demonstrate understanding of the
differences among linear units, square units and cubic units.
M5. Make conversions within the same
measurement system while performing computations.
M6. Use strategies to develop formulas for
determining perimeter and area of triangles, rectangles and parallelograms, and
volume of rectangular prisms.
M7. Use benchmark angles (e.g.; 45, 90,
120) to estimate the measure of angles, and use a tool to measure and draw
angles.
Geometry
and Spatial Sense
G1. Draw circles, and identify and
determine relationships among the radius, diameter, center and circumference;
e.g., radius is half the diameter, the ratio of the circumference of a circle
to its diameter is an approximation of .
G2. Use standard language to describe line,
segment, ray, angle, skew, parallel and perpendicular.
G3. Label vertex, rays, interior and
exterior for an angle.
G4. Describe and use properties of
congruent figures to solve problems.
G5. Use physical models to determine the
sum of the interior angles of triangles and quadrilaterals.
G6. Extend understanding of coordinate
system to include points whose x or y values may be negative numbers.
G7. Understand that the measure of an angle
is determined by the degree of rotation of an angle side rather than the length
of either side.
Patterns,
Functions, and Algebra
A1. Justify a general rule for a pattern or
a function by using physical materials, visual representations, words, tables
or graphs.
A2. Use calculators or computers to develop
patterns, and generalize them using tables and graphs.
A3. Use variables as unknown quantities in
general rules when describing patterns and other relationships.
A4. Create and interpret the meaning of
equations and inequalities representing problem situations.
A5. Model problems with physical materials
and visual representations, and use models, graphs and tables to draw
conclusions and make predictions.
A6. Describe how the quantitative change in
a variable affects the value of a related variable; e.g., describe how the rate
of growth varies over time, based upon data in a table or graph.
Data
Analysis and Probability
D1. Read, construct and interpret frequency
tables, circle graphs and line graphs.
D2. Select and use a graph that is
appropriate for the type of data to be displayed; e.g., numerical vs.
categorical data, discrete vs. continuous data.
D3. Read and interpret increasingly complex
displays of data, such as double bar graphs.
D4. Determine appropriate data to be
collected to answer questions posed by students or teacher, collect and display
data, and clearly communicate findings.
D5. Modify initial conclusions, propose and
justify new interpretations and predictions as additional data are collected.
D6. Determine and use the range, mean,
median and mode, and explain what each does and does not indicate about the set
of data.
D7. List and explain all possible outcomes
in a given situation.
D8. Identify the probability of events
within a simple experiment, such as three chances out of eight.
D9. Use 0, 1 and ratios between 0 and 1 to
represent the probability of outcomes for an event, and associate the ratio
with the likelihood of the outcome.
D10. Compare what should happen
(theoretical/expected results) with what did happen (experimental/actual
results) in a simple experiment.
D11. Make predictions based on experimental
and theoretical probabilities.
Investigations units –
all grades
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