Grade 5 Correlation of Core Knowledge® and New York Learning Standards

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Music -Students will compose original music and perform music written by others. They will understand and use the basic elements of music in their performances and compositions. Students will engage in individual and group musical and music-related tasks, and will describe the various roles and means of creating, performing, recording, and producing music.


•create short pieces consisting of sounds from a variety of traditional (e.g., tambourine, recorder, piano, voice), electronic (e.g., keyboard), and nontraditional sound sources (e.g., water-filled glasses) (a)

•sing songs and play instruments, maintaining tone quality, pitch, rhythm, tempo, and dynamics; perform the music expressively; and sing or play simple repeated patterns (ostinatos) with familiar songs, rounds, partner songs, and harmonizing parts (b)

•read simple standard notation in performance, and follow vocal or keyboard scores in listening (c)

•in performing ensembles, read very easy/easy music (New York State School Music Association [NYSSMA] level I-II)1 and respond appropriately to the gestures of the conductor

•identify and use, in individual and group experiences, some of the roles, processes, and actions used in performing and composing music of their own and others (e).

II. Listening and Understanding

A. Composers and Their Music

• Ludwig van Beethoven, Symphony No. 5

• Modest Mussorgsky, Pictures at an Exhibition (as orchestrated by Ravel)
B. Musical Connections

• Music from the Renaissance (such as choral works of Josquin Desprez; lute songs by John Dowland)

• Felix Mendelssohn, Overture, Scherzo, and Wedding March from A Midsummer Night’s Dream

Standard 2: Knowing and Using Arts Materials and Resources
2. Music- Students will use traditional instruments, electronic instruments, and a variety of nontraditional sound sources to create and perform music. They will use various resources to expand their knowledge of listening experiences, performance opportunities, and/or information about music. Students will identify opportunities to contribute to their communities’ music institutions, including those embedded in other institutions (church choirs, industrial music ensembles, etc.). Students will know the vocations and avocations available to them in music.


•use classroom and nontraditional instruments in performing and creating music (a)

•construct instruments out of material not commonly used for musical instruments (b)

•use current technology to manipulate sound (c)

•identify the various settings in which they hear music and the various resources that are used to produce music during a typical week; explain why the particular type of music was used (d)

•demonstrate appropriate audience behavior, including attentive listening, in a variety of musical settings in and out of school (e)

•discuss ways that music is used by various members of the community (f).

III. American Musical Traditions

• Spirituals

Originated by African-Americans, many spirituals go back to the days of slavery.

Familiar spirituals, such as:

Down by the Riverside

Sometimes I Feel Like a Motherless Child

Wayfaring Stranger

We Shall Overcome

Standard 4: Understanding the Cultural Dimensions and Contributions of the Arts

4. Music- Students will develop a performing and listening repertoire of music of various genres, styles, and cultures that represent the peoples of the world and their manifestations in the United States. Students will recognize the cultural features of a variety of musical compositions and performances and understand the functions of music within the culture.

•identify the cultural contexts of a performance or recording and perform (with movement , where culturally appropriate) a varied repertoire of folk , art and contemporary selections form the basic cultures that represent the peoples of the world (a)

•identify from a performance or recording the titles and composers of well-known examples of classical concert music and blues/jazz selections (b)

•discuss the current and past primary cultural, social, and political uses for the music they listen to and perform (c).

•in performing ensembles, read and perform repertoire in a culturally authentic manner (d)

IV. Songs

Battle Hymn of the Republic

Danny Boy

Dona Nobis Pacem (round)

Git Along Little Dogies

God Bless America


The Happy Wanderer

Havah Nagilah

If I Had a Hammer

Red River Valley



Sweet Betsy from Pike

Standard 3: Responding to and Analyzing Works of Art
3. Music- Students will demonstrate the capacity to listen to and comment on music. They will relate their critical assertions about music to its aesthetic, structural, acoustic, and psychological qualities. Students will use concepts based on the structure of music’s content and context to relate music to other broad areas of knowledge. They will use concepts from other disciplines to enhance their understanding of music.


•through listening, identify the strengths and weaknesses of specific musical works and performances, including their own and others’ (a)

•describe the music in terms related to basic elements such as melody, rhythm, harmony, dynamics, timbre, form, style, etc. (b)

•discuss the basic means by which the voice and instruments can alter pitch, loudness, duration, and timbre (c)

•describe the music’s context in terms related to its social and psychological functions and settings (e.g., roles of participants, effects of music, uses of music with other events or objects, etc.) (d)

•describe their understandings of particular pieces of music and how they relate to their surroundings (e).

The specific content outlined in the Core Knowledge Sequence constitutes a solid foundation of knowledge in each subject area.  It is also critically important to establish a similar sequential program in Mathematics, structured to provide guided practice in various formats and frequent review throughout the year.  Mathematics programs that follow sound cognitive principles and therefore lead to greater student mastery are:  Singapore Math, Saxon Math, and Direct Instruction Mathematics.  


I. Numbers and Number Sense

• Read and write numbers (in digits and words) up to the billions.

• Recognize place value up to billions.

• Order and compare numbers to 999,999,999 using the signs <, >, and = .

• Write numbers in expanded form.

• Integers

Locate positive and negative integers on a number line.

Compare integers using the symbols <, >, = .

Know that the sum of an integer and its opposite is 0.

Add and subtract positive and negative integers.

• Using a number line, locate positive and negative whole numbers.

Round to the nearest ten; to the nearest hundred; to the nearest thousand; to the nearest hundred-thousand.

• Exponents

Review perfect squares and square roots to 144; recognize the square root sign, √——.

Using the terms squared and cubed and to the nth power, read and evaluate numerical expressions with exponents.

Identify the powers of ten up to 106.

• Identify a set and the members of a set, as indicated by { }.

• Identify numbers under 100 as prime or composite.

• Identify prime factors of numbers to 100 and write using exponential notation for multiple primes.

• Determine the greatest common factor (GCF) of given numbers.

• Determine the least common multiple (LCM) of given numbers.
II. Ratio and Percent

A. Ratio

• Determine and express simple ratios.

• Use ratio to create a simple scale drawing.

• Ratio and rate: solve problems on speed as a ratio, using the formula

S = d/t (or D = r x t).
B. Percent

• Recognize the percent sign (%) and understand percent as “per hundred.”

• Express equivalences between fractions, decimals, and percents, and know

common equivalences:

1/10 = 10%

¼ = 25%

½ = 50%

¾ = 75%

• Find the given percent of a number.
III. Fractions and Decimals

A. Fractions

• Determine the least common denominator (LCD) of fractions with unlike denominators.

• Recognize equivalent fractions (for example, ½ = 3/6).

• Put fractions in lowest terms.

• Compare fractions with like and unlike denominators, using the signs <, >, and = .

• Identify the reciprocal of a given fraction; know that the product of a given number and its reciprocal = 1.

• Add and subtract mixed numbers and fractions with like and unlike denominators.

• Multiply and divide fractions.

• Add and subtract fractions with like and unlike denominators.

• Add and subtract mixed numbers and fractions; multiply mixed numbers and fractions.

• Round fractions to the nearest whole number.

• Write fractions as decimals (e.g., ¼ = 0.25; 17/25 = 0.68; 1/3 = 0.3333. . . or 0.33, rounded to the nearest hundredth).

B. Decimals

• Read, write, and order decimals to the nearest ten-thousandth.

• Write decimals in expanded form.

• Read and write decimals on a number line.

• Round decimals (and decimal quotients) to the nearest tenth; to the nearest hundredth; to the nearest thousandth.

• Estimate decimal sums, differences, and products by rounding.

• Add and subtract decimals through ten-thousandths.

• Multiply decimals: by 10, 100, and 1,000; by another decimal.

• Divide decimals by whole numbers and decimals.

Standard 3: Number and Numeration

2. Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.


•use whole numbers and fractions to identify locations, quantify groups of objects, and measure distances.

•use concrete materials to model numbers and number relationships for whole numbers and common fractions, including decimal fractions.

•relate counting to grouping and to place-value.

•recognize the order of whole numbers and commonly used fractions and decimals.

•demonstrate the concept of percent through problems related to actual situations.

IV. Computation

A. Addition

• Commutative and associative properties: know the names and understand the properties.

B. Multiplication

• Commutative, associative, and distributive properties: know the names and understand the properties.

• Multiply two factors of up to four digits each.

• Write numbers in expanded form using multiplication.

• Estimate a product.

• Use mental computation strategies for multiplication, such as breaking a problem into partial products, for example: 3 x 27 = (3 x 20) + (3 x 7) = 60 + 21 = 81.

• Solve word problems involving multiplication.
C. Division

• Understand multiplication and division as inverse operations.

• Know what it means for one number to be “divisible” by another number.

• Know that you cannot divide by 0; that any number divided by 1 = that number.

• Estimate the quotient.

• Know how to move the decimal point when dividing by 10, 100, or 1,000.

• Divide dividends up to four digits by one-digit, two-digit, and three-digit divisors.

• Solve division problems with remainders; round a repeating decimal quotient.

• Check division by multiplying (and adding remainder).
D. Solving Problems and Equations

• Solve word problems with multiple steps.

• Solve problems with more than one operation.

Standard 3: Operations

3. Students use mathematical operations and relationships among them to understand mathematics.


•add, subtract, multiply, and divide whole numbers.

•develop strategies for selecting the appropriate computational and operational method in problem-solving situations.

•know single digit addition, subtraction, multiplication, and division facts.

•understand the commutative and associative properties.

V. Measurement

• Convert to common units in problems involving addition and subtraction of different units.

• Time: Solve problems on elapsed time; regroup when multiplying and dividing amounts of time.

Standard 3: Measurement

5. Students use measurement in both metric and English measure to provide a major link between the abstractions of mathematics and the real world in order to describe and compare objects and data.


•understand that measurement is approximate, never exact.

•select appropriate standard and nonstandard measurement tools in measurement activities.

•understand the attributes of area, length, capacity, weight, volume, time, temperature, and angle.

•estimate and find measures such as length, perimeter, area, and volume using both nonstandard and standard units.

•collect and display data.

•use statistical methods such as graphs, tables, and charts to interpret data.

VI. Geometry

Identify and draw points, segments, rays, lines.

• Identify and draw lines: horizontal; vertical; perpendicular; parallel; intersecting.

• Measure the degrees in angles, and know that

right angle = 90°

acute angle: less than 90°

obtuse angle: greater than 90°

straight angle = 180°

• Identify and construct different kinds of triangles: equilateral, right, and isosceles.

• Know what it means for triangles to be congruent.

• Identify polygons:

triangle, quadrilateral, pentagon, hexagon, and octagon

parallelogram, trapezoid, rhombus, rectangle, square

• Know that regular polygons have sides of equal length and angles of equal measure.

• Identify and draw diagonals of polygons.

• Circles

Identify arc, chord, radius (plural: radii), and diameter (radius = !s diameter).

Using a compass, draw circles with a given diameter or radius.

Find the circumference of a circle using the formulas C = πd, and C = 2 πr, using 3.14 as the value of pi.

• Area

Review the formula for the area of a rectangle (Area = length x width) and solve problems involving finding area in a variety of square units (such as mi2; yd2; ft2; in2; km2; m2; cm2; mm2).

Find the area of triangles, using the formula A = ½(b x h).

Find the area of a parallelogram using the formula A = b x h.

Find the area of an irregular figure (such as a trapezoid) by dividing into regular figures for which you know how to find the area.

Compute volume of rectangular prisms in cubic units (cm3, in3), using the formula

V = l x w x h.

Find the surface area of a rectangular prism.

Standard 3: Patterns/Functions

7. Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics, and construct generalizations that describe patterns simply and efficiently.


•recognize, describe, extend, and create a wide variety of patterns.

•represent and describe mathematical relationships.

•explore and express relationships using variables and open sentences.

•solve for an unknown using manipulative materials.

•use a variety of manipulative materials and technologies to explore patterns.

•interpret graphs.

•explore and develop relationships among two- and three-dimensional geometric shapes.

•discover patterns in nature, art, music, and literature.

Standard 3: Modeling/Multiple Representation

4. Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating, and connecting mathematical information and relationships.


•use concrete materials to model spatial relationships.

•construct tables, charts, and graphs to display and analyze real-world data.

•use multiple representations (simulations, manipulative materials, pictures, and diagrams) as tools to explain the operation of everyday procedures.

•use variables such as height, weight, and hand size to predict changes over time.

•use physical materials, pictures, and diagrams to explain mathematical ideas and processes and to demonstrate geometric concepts.

VII. Probability and Statistics

• Understand probability as a measure of the likelihood that an event will happen; using simple models, express probability of a given event as a fraction, as a percent, and as a decimal between 0 and 1.

• Collect and organize data in graphic form (bar, line, and circle graphs).

• Solve problems requiring interpretation and application of graphically displayed data.

• Find the average (mean) of a given set of numbers.

• Plot points on a coordinate plane, using ordered pairs of positive and negative whole numbers.

• Graph simple functions.

Standard 3: Uncertainty

6. Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.


•make estimates to compare to actual results of both formal and informal measurement.

•make estimates to compare to actual results of computations.

•recognize situations where only an estimate is required.

•develop a wide variety of estimation skills and strategies.

•determine the reasonableness of results.

•predict experimental probabilities.

•make predictions using unbiased random samples.

•determine probabilities of simple events.

VIII. Pre-Algebra

• Recognize variables and solve basic equations using variables.

• Write and solve equations for word problems.

• Find the value of an expression given the replacement values for the variables, for example: What is 7 - c if c is 3.5?

This Core Knowledge topic goes above the New York Learning Standards.

These standards are ongoing mathematics process skills.

Standard 3: Mathematical Reasoning

1. Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence, and construct an argument.


•use models, facts, and relationships to draw conclusions about mathematics and explain their thinking.

•use patterns and relationships to analyze mathematical situations.

•justify their answers and solution processes.

•use logical reasoning to reach simple conclusions.

Standard 1: Analysis, Inquiry, and Design; Mathematical Analysis

1. Abstraction and symbolic representation are used to communicate mathematically


•use special mathematical notation and symbolism to communicate in mathematics and to compare and describe quantities, express relationships, and relate mathematics to their immediate environments.

Standard 1: Analysis, Inquiry, and Design; Mathematical Analysis

2. Deductive and inductive reasoning are used to reach mathematical conclusions.


•use simple logical reasoning to develop conclusions, recognizing that patterns and relationships present in the environment assist them in reaching these conclusions.

Standard 1: Analysis, Inquiry, and Design; Mathematical Analysis

3. Critical thinking skills are used in the solution of mathematical problems.

•explore and solve problems generated from school, home, and community situations, using concrete objects or manipulative materials when possible.


I. Classifying Living Things

• Scientists have divided living things into five large groups called kingdoms, as follows:



Fungus (mushrooms, yeast, mold, mildew)

Protist (algae, protozoans, amoeba, euglena)

Moneran (bacteria, blue-green algae)

• Each kingdom is divided into smaller groupings as follows:







Species (Variety)

• When classifying living things, scientists use special names made up of Latin words (or words made to sound like Latin words), which help scientists around the world understand each other and ensure that they are using the same names for the same living things.

Homo sapiens: the scientific name for the species to which human beings belong (genus Homo, species sapiens)

Taxonomists: biologists who specialize in classification

• Different classes of vertebrates and major characteristics: fish, amphibians, reptiles, birds, mammals (review from grade 3)
II. Cells: Structures and Processes

• All living things are made up of cells.

• Structure of cells (both plant and animal)

Cell membrane: selectively allows substances in and out

Nucleus: surrounded by nuclear membrane, contains genetic material, divides for reproduction

Cytoplasm contains organelles, small structures that carry out the chemical activities of the cell, including mitochondria (which produce the cell’s energy) and vacuoles (which store food, water, or wastes).

• Plant cells, unlike animal cells, have cell walls and chloroplasts.

• Cells without nuclei: monerans (bacteria)

• Some organisms consist of only a single cell: for example, amoeba, protozoans, some algae.

• Cells are shaped differently in order to perform different functions.

• Organization of cells into tissues, organs, and systems:

In complex organisms, groups of cells form tissues (for example, in animals, skin tissue or muscle tissue; in plants, the skin of an onion or the bark of a tree).

Tissues with similar functions form organs (for example, in some animals, the heart, stomach, or brain; in some plants, the root or flower).

In complex organisms, organs work together in a system (recall, for example, from earlier studies of the human body, the digestive, circulatory, and respiratory systems).

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