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THIRD GRADE READING CURRICULUM
The primary focus of the reading curriculum in the Archdiocese of Kansas City in Kansas is to maximize the talents in our students so they may become proficient and infotmed critical readers in God's ever changing world.
STANDARD 1: READING The student will read and comprehend text across the curriculum including Bible Scripture.
Phonetic Clues
The student will:
I. Be able to: Use rhyming words to make word families. Apply long vowel rules.
2. Be able to use: Consonant clusters Consonant digraphs Variant vowel sounds +
3. Distinguish: r controlled vowels + Hard/soft c and g +
Structural Analysis
The student will:
I. Identify and form: Plurals + Compound words + Contractions +
2. Recognize base (root) words, suffixes, and prefixes. 3. Apply rules of syllabication to decode unfamiliar words. (see Appendix A)
Vocabulary
The student will:
I. Read the following basic sight words. +
about cut far hold
Apostle done find hot
better draw full hurt
both drink gospel if
bring fall got keep
carry clean grow liturgy
laugh only show
light own small
long pick spirit
much rosary start
myself scripture today
never shall
together
2. Name and understand text by using: Selection vocabulary Vocabulary expansion across the curriculum
3. Determine word meaning by using: Context clues e.g. definitions, restatements, examples A. Prior knowledge Homophones/homographs Synonyms/antonyms + Word structure e.g. compound nouns, root words, prefixes, suffixes A
Comprehension
The student will:
1. Demonstrate comprehension of a written selection by applying the various strategies listed below:
Literal Inferential
Sequence Main idea Topic+ A (unstated) Main idea A. Making Recall details A inferences and Cause/effect drawing Picture clues conclusions A Compare/contrast A. Pronoun referents
Compare/contrast ...
Study Strategies
The student will:
Critical Response
Fact/opinion Retell a story A. Prior knowledge Generate questions Drawing Drawing/singing/acting conclusions/generalizations Discussion Evaluation/judgments Writing Author's purpose Following written/oral Visualization/imagery directions Problem solving Summarizing Paraphrasing
Links causes and Identifies text structures of effects A. sequence, problem/solution, compare/contrast, description, cause/effect A
I. Select and apply the following study strategies by developing oral meaning and writing a simple report:
Alphabetize to the 3rd letter + Locate words in dictionary/glossary Interpret information from graphic aids (see Reading Framework) Book Parts+ (see Reading Framework) Pause and reflect Encyclopedia, atlas Research Note taking skills Resource materials Skim/scan Technology
2. Transfer reading strategies across curricula.
Literature Components
The student will:
1. Analyze literature by using the various literature components: Setting + Main character A Relationships between characters A Problem/conflict Character motivation Plot: beginning, middle, end.
Literary Devices Stylistic Devices
Refrain Rhyme+
Repetition+ Dialogue
Rhythm AlliteratOnomatopoeiaion
Genre
The student will:
Figures of Speech Other
Personification Simile Hyperbole
Point of View Theme
1. Distinguish and recognize a variety of authors, cultures, and genre. (see Appendix B)
Fiction Nonfiction Bible
2. Be able to identify different text type: narrative, expository, persuasion, technical.
Reading Fluency
The student will:
I. Develop oral reading skills by practicing: Expression Projection Fluency Sustained oral reading Sustained silent reading
Supplemental/Independent Reading
The student will:
1. Listen to, select, read, and respond to reading materials.
STANDARD 2: LITERATURE The student will respond to a variety of text and identify Catholic moral values and/or teaching of our Catholic faith.
• Literature is infused with Catholic values. NCEA has developed a list of books that promote Catholic values. See the NCEA Working Booklist.
STANDARD 3: WRITING The student will write effectively for a variety of audiences, purposes, and contexts.
• Writing is infused with Catholic values. See the Language Arts curriculum.
STANDARD 4: RESEARCH The student will apply reading and writing skills to demonstrate learning.
The student will:
1. Use effective research practices. 2. Use ethical research practices.
+Denotes mastery (see Appendix B)
,~d
~~Kansas Common Core Standards ,..,-
Note: See page 10 of the cess document for the "Note on range and content of student reading" for grades K-5. See page 35 of the cess document for the "Note on range and content of student reading" for grades 6-12.
Grade 3
Reading Standards for Literature RL.3.1- Ask and answer questions to demonstrate understanding of a text, referring explicitly to the text as the basis for the answers.
Key Ideas and RL.3.2- Recount stories, including fables, folktales, and myths from diverse cultures; determine
Details the central message, lesson, or moral and explain how it is conveyed through key details in the text. RL.3.3- Describe characters in a story (e.g., their traits, motivations, or feelings) and explain how their actions contribute to the sequence of events. RL.3.4- Determine the meaning of words and phrases as they are used in a text, distinguishing literal from nonliterallanguage.
Craft and RL.3.5- Refer to parts of stories, dramas, and poems when writing or speaking about a text, using Structure terms such as chapter, scene, and stanza; describe how each successive part builds on earlier
sections. RL.3.6- Distinguish their own point of view from that of the narrator or those of the characters. RL.3.7- Explain how specific aspects of a text's illustrations contribute to what is conveyed by the
Integration of words in a story (e.g., create mood, emphasize aspects of a character or setting). Knowledge (Not applicable to literature)
and Ideas RL.3.9- Compare and contrast the themes, settings, and plots of stories written by the same author about the same or similar characters (e.g., in books from a series).
Range of RL.3.10- By the end of the year, read and comprehend literature, including stories, dramas, and
Reading and poetry, at the high end of the grades 2-3 text complexity band independently and proficiently.
Level of Text Complexity
This document was adapted from the Common Core State Standards (CCSS) for use in Kansas. To access the full cess document, which includes important supplemental information and several appendices, please visit www.corestandards.org.
3/26/12
~irt ·~:;:Kansas Common Core Standards ~-""
Grade 3
Reading Standards for Informational Text Key Ideas and Rl.3.1- Ask and answer questions to demonstrate understanding of a text, referring explicitly to
Details the text as the basis for the answers. Rl.3.2- Determine the main idea of a text; recount the key details and explain how they support the main idea. Rl.3.3- Describe the relationship between a series of historical events, scientific ideas or concepts, or steps in technical procedures in a text, using language that pertains to time, sequence, and cause/effect.
Craft and Rl.3.4- Determine the meaning of general academic and domain-specific words and phrases in a
Structure text relevant to a grade 3 topic or subject area. Rl.3.5- Use text features and search tools (e.g., key words, sidebars, hyperlinks) to locate information relevant to a given topic efficiently. Rl.3.6- Distinguish their own point of view from that of the author of a text.
Integration of Rl.3.7- Use information gained from illustrations (e.g., maps, photographs) and the words in a
Knowledge text to demonstrate understanding of the text (e.g., where, when, why, and how key events
and Ideas occur). Rl.3.8- Describe the logical connection between particular sentences and paragraphs in a text (e.g., comparison, cause/effect, first/second/third in a sequence). Rl.3.9- Compare and contrast the most important points and key details presented in two texts on the same topic.
Range of Rl.3.10- By the end of the year, read and comprehend informational texts, including
Reading and history/social studies, science, and technical texts, at the high end ofthe grades 2-3 text
Level of Text complexity band independently and proficiently.
Complexity
This document was adapted from the Common Core State Standards {CCSS) for use in Kansas. To access the full cess document, which includes important supplemental information and several appendices, please visit www.corestandards.org.
3/26/12
"if' ;1.~ Kansas Common Core Standards .;y-,._··
Grade 3
Reading Standards: Foundational Skills RF.3.1- Know and apply grade-level phonics and word analysis skills in decoding words.
Phonics and RF.3.1a- Identify and know the meaning of the most common prefixes and derivational
suffixes. Word
RF.3.1b- Decode words with common Latin suffixes. Recognition
RF.3.1c- Decode multisyllable words. RF.3.1d- Read grade-appropriate irregularly spelled words.
RF.3.2- Read with sufficient accuracy and fluency to support comprehension.
RF.3.2a- Read on-level text with purpose and understanding.
Fluency RF.3.2b- Read on-level prose and poetry orally with accuracy, appropriate rate, and expression on successive readings.
RF.3.2c- Use context to confirm or self-correct word recognition and understanding, rereading as necessary.
This document was adapted from the Common Core State Standards (CCSS) for use in Kansas. To access the full CCSS document, which includes important supplemental information and several appendices, please visit www.corestandards.org.
3/26/12
't~l ~_Kansas Common Core Standards
p ~ ,,
Note: See page 18 of the cess document for the "Note on range and content of student writing" for grades K-5. See page 41 of the cess document for the "Note on range and content of student writing" for grades 6-12.
Grade 3
Writing Standards W.3.1- Write opinion pieces on topics or texts, supporting a point of view with reasons.
W.3.1a -Introduce the topic or text they are writing about, state an opinion, and create an organizational structure that lists reasons.
W.3.1b- Provide reasons that support the opinion.
W.3.1c- Use linking words and phrases (e.g., because, therefore, since, for example) to connect opinion and reasons.
W.3.1d- Provide a concluding statement or section.
W.3.2- Write informative/explanatory texts to examine a topic and convey ideas and information clearly.
W.3.2a -Introduce a topic and group related information together; include illustrations when
Text Types and useful to aiding comprehension.
Purposes W.3.2b- Develop the topic with facts, definitions, and details.
W.3.2c- Use linking words and phrases (e.g., also, another, and, more, but) to connect ideas within categories of information.
W.3.2d- Provide a concluding statement or section.
W.3.3- Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences.
W.3.3a- Establish a situation and introduce a narrator and/or characters; organize an event sequence that unfolds naturally.
W.3.3b- Use dialogue and descriptions of actions, thoughts, and feelings to develop experiences and events or show the response of characters to situations.
W.3.3c- Use temporal words and phrases to signal event order. W.3.3d- Provide a sense of closure.
W.3.4- With guidance and support from adults, produce writing in which the development and organization are appropriate to task and purpose. (Grade-specific expectations for writing types
Production and are defined in standards 1-3 above.)
Distribution of W.3.5- With guidance and support from peers and adults, develop and strengthen writing as needed by planning, revising, and editing. (Editing for conventions should demonstrate
Writing command of Language standards 1-3 up to and including grade 3 on pages 28 and 29 [of the cess].) W.3.6- With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others.
Research to W.3.7- Conduct short research projects that build knowledge about a topic.
Build and W.3.8- Recall information from experiences or gather information from print and digital
Present sources; take brief notes on sources and sort evidence into provided categories. W.3.9- (Begins in grade 4)
This document was adapted from the Common Core State Standards (CCSS) for use in Kansas. To access the full cess document, which includes important supplemental information and several appendices, please visit www.corestandards.org.
3/26/12
~ •. j d
"';;.~:Kansas Common Core Standards
Knowledge
Range of W.3.10- Write routinely over extended time frames (time for research, reflection, and revision)
Writing and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
Anchor Standards for Speaking and Listening
According the cess document, the "standards on the following pages define what students should understand and be able to do by the end of each grade. They correspond to the College and Career Readiness (CCR) anchor standards below by number. The CCR and grade-specific standards are necessary complements-the former providing broad standards, the latter providing additional specificity-that together define the skills and understandings that all students must demonstrate."
College and Career Readiness Anchor Standards for Speaking and Listening Prepare for and participate effectively in a range of conversations and collaborations
Comprehension 1 with diverse partners, building on others' ideas and expressing their own clearly and
and persuasively.
Collaboration 2 Integrate and evaluate information presented in diverse media and formats, including visually, quantitatively, and orally.
3 Evaluate a speaker's point of view, reasoning, and use of evidence and rhetoric. Present information, findings, and supporting evidence such that listeners can follow the
Presentation 4 line of reasoning and the organization, development, and style are appropriate to task,
of Knowledge purpose, and audience. Make strategic use of digital media and visual displays of data to express information
and Ideas 5 and enhance understanding of presentations.
6 Adapt speech to a variety of contexts and communicative tasks, demonstrating command of formal English when indicated or appropriate.
Note: See page 22 of the cess document for the "Note on range and content of student speaking and listening" for grades K-5. See page 48 ofthe CCSS document for the "Note on range and content of student speaking and listening" for grades 6-12.
This document was adapted from the Common Core State Standards (CCSS) for use in Kansas. To access the full cess document, which includes important supplemental information and several appendices, please visit www.corestandards.org.
3/26/12
:; ~./ ~Kansas Common Core Standards
Grade 3
Speaking and Listening Standards
SL3.1- Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 3 topics and texts, building on others' ideas and expressing their own clearly.
SL.3.1a- Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion.
Comprehension SL.3.1b- Follow agreed-upon rules for discussions (e.g., gaining the floor in respectful ways,
listening to others with care, speaking one at a time about the topics and texts under & Collaboration discussion).
SL.3.1c- Ask questions to check understanding of information presented, stay on topic, and link their comments to the remarks of others.
SL.3.1d- Explain their own ideas and understanding in light of the discussion. SL3.2- Determine the main ideas and supporting details of a text read aloud or information presented in diverse media and formats, including visually, quantitatively, and orally. SL3.3- Ask and answer questions about information from a speaker, offering appropriate elaboration and detail. SL3.4- Report on a topic or text, tell a story, or recount an experience with appropriate facts and relevant, descriptive details, speaking clearly at an understandable pace.
Presentation of SL3.5- Create engaging audio recordings of stories or poems that demonstrate fluid reading at
Knowledge and an understandable pace; add visual displays when appropriate to emphasize or enhance certain
Ideas facts or details. SL3.6- Speak in complete sentences when appropriate to task and situation in order to provide requested detail or clarification. (See grade 3 Language standards 1 and 3 on page 26 [of the cess] for specific expectations.)
This document was adapted from the Common Core State Standards {CCSS) for use in Kansas. To access the full cess document, which includes important supplemental information and several appendices, please visit www.corestandards.org.
3/26/12
"-~I ~_~..,,d!,:: Kansas Common Core Standards (l'r'l
Grade 3
Note: Beginning in grade 3, skills and understandings that are particularly likely to require continued attention in higher grades as they are applied to increasingly sophisticated writing and speaking are marked with an asterisk(*). See the table on page 30 [of the CCSS] for a complete list and Appendix A [of the CCSS] for an example of how these skills develop in sophistication.
Language Standards L.3.1- Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.
L.3.1a- Explain the function of nouns, pronouns, verbs, adjectives, and adverbs in general and their functions in particular sentences.
L.3.1b- Form and use regular and irregular plural nouns.
L.3.1c- Use abstract nouns (e.g., childhood).
L.3.1d- Form and use regular and irregular verbs.
L.3.1e- Form and use the simple (e.g., I walked; I walk; I will walk) verb tenses.
L.3.1f- Ensure subject-verb and pronoun-antecedent agreement.*
L.3.1g- Form and use comparative and superlative adjectives and adverbs, and choose
Conventions of between them depending on what is to be modified.
L.3.1h- Use coordinating and subordinating conjunctions. Standard L.3.1i- Produce simple, compound, and complex sentences.
English L.3.2- Demonstrate command of the conventions of standard English capitalization, punctuation, and spelling when writing.
L.3.2a- Capitalize appropriate words in titles.
L.3.2b- Use commas in addresses.
L.3.2c- Use commas and quotation marks in dialogue.
L.3.2d- Form and use possessives.
L.3.2e- Use conventional spelling for high-frequency and other studied words and for adding suffixes to base words (e.g., sitting, smiled, cries, happiness).
L.3.2f- Use spelling patterns and generalizations (e.g., word families, position-based spellings, syllable patterns, ending rules, meaningful word parts) in writing words.
L.3.2g- Consult reference materials, including beginning dictionaries, as needed to check and correct spellings.
l.3.3- Use knowledge of language and its conventions when writing, speaking, reading, or Knowledge of listening.
Language l.3.3a- Choose words and phrases for effect.* L.3.3b- Recognize and observe differences between the conventions of spoken and written
standard English.
This document was adapted from the Common Core State Standards (CCSS) for use in Kansas. To access the full cess document, which includes important supplemental information and several appendices, please visit www.corestandards.org.
3/26/12
'\~I ~£Kansas Common Core Standards
""'" - ,_, ___ ,.·.··
L3.4- Determine or clarify the meaning of unknown and multiple-meaning word and phrases based on grade 3 reading and content, choosing flexibly from a range of strategies.
L.3.4a- Use sentence-level context as a clue to the meaning of a word or phrase.
L.3.4b- Determine the meaning of the new word formed when a known affix is added to a known word (e.g., agreeable/disagreeable, comfartable/uncomfortable, care/careless, heat/preheat).
L.3.4c- Use a known root word as a clue to the meaning of an unknown word with the same root (e.g., company, companion).
Vocabulary L.3.4d- Use glossaries or beginning dictionaries, both print and digital, to determine or clarify
Acquisition and the precise meaning of key words and phrases.
Use L3.5- Demonstrate understanding of word relationships and nuances in word meanings.
L.3.5a- Distinguish the literal and non literal meanings of words and phrases in context (e.g., take steps).
L.3.5b -Identify real-life connections between words and their use (e.g., describe people who are friendly or helpful).
L.3.5c- Distinguish shades of meaning among related words that describe states of mind or degrees of certainty (e.g., knew, believed, suspected, heard, wondered).
L3.6- Acquire and use accurately grade-appropriate conversational, general academic, and domain-specific words and phrases, including those that signal spatial and temporal relationships (e.g., After dinner that night we went looking for them).
This document was adapted from the Common Core State Standards (CCSS) for use in Kansas. To access the full cess document, which includes important supplemental information and several appendices, please visit www.corestandards.org.
3/26/12
SIXTH GRADE MATH CURRICULUM
The primary focus of Math in the Archdiocese of Kansas City in Kansas is to promote in our students their problem solving abilities, which are among God's many gifts.
Standard 1: Number and Computation
The student will:
I. Solve problems with fractions, decimals, and percents. (Use weekly bulletin to comprise average donations to Church.)
2. A Compare and order integers, fractions greater than or equal to zero, and decimals greater than or equal to zero through thousandths place.
3. A Know and explain numerical relationships between percents, decimals, and fractions between 0 and 1 (e.g. recognizing that percent means out of 100 so 60% means 60 out of a hundred, 60% is .60, and 60% is 60/100 as a fraction.
4. A Estimate to check whether or not the result of a real-world problem using rational numbers and/or the irrational number pi is reasonable and makes predictions based on the information.
5. A Perform and explain these computations: a. Divides whole numbers through a 2-digit divisor and a four-digit dividend
and expresses the remainder as whole number, fraction, or decimal. b. Adds, subtracts, and multiplies fractions expressing answer in simplest
form. 6. A Solve real-world problems using addition, subtraction, multiplication, and
division of decimals through hundredths place. 7. Know divisibility rules for 2,3,5,6,9, and 10. 8. Use exponents to show prime factorization. 9. Identify natural, whole, integers, rational, and irrational numbers. I 0. Identify and apply the inverse properties of addition and multiplication. II. Apply the zero property of multiplication. 12. Square and cube numbers. 13. Use positive, negative, and zero exponents. 14. OGenerate and solve real-world problems using equivalent representations of
integers, fractions, and decimals. 15. OPerform and explain these computations: add/subtract decimals from millions
place through thousandths place, and multiply and divide a four-digit number by a two-digit number with decimals.
16. OFind a whole number percent (between 0 and 1 00) of a whole number such as 12% of 40 is what number?
Standard 2: Algebra
The student will
1. A State the rule to find the next number of a pattern with one operational change (addition, subtraction, multiplication, and division) to move between consecutive
terms (e.g. given 4,8,and 16, double the number to get the next term or multiply the term by two to get the next number). (Read Exo 25:40 for pattern)
2. A Write and/or solve one-step equations (e.g. a player scored three more points today than yesterday. How many points were scored yesterday? Write an equation to represent this problem. The equation would bey+ 3 = 17. y=l4.
3. Explain and use equality and inequality symbols. 4. Recognize the difference among expressions, equations, and inequalities. 5. Use algebraic expressions and order of operations. 6. Translate word expressions into algebraic expressions. 7. Solve problems using formulas. 8. Compute with ratio/proportion within algebraic expressions and order of
operations. 9. OFind the value of algebraic expressions using whole numbers such as: If x=3,
then 5x=5(3) 10. OKnow, use, and explain math relationships with models such as place value
charts, hundred charts, faction and mixed number models, and base ten blocks. II. OKnow and use equations and inequalities to model numerical relationships.
Standard 3: Geometry
Teacher note: The term "geometry" comes from the Greek words meaning, "earth measure." The process of learning to measure at the early grades focuses on what property (length, width, height) is to be measured and to make comparisons.
The student will:
I. Demonstrate counting back change. (Value: honesty) 2. A Classify angles as right, obtuse, acute, or straight and triangles as right, obtuse,
scalene, isosceles, and equilateral. 3. .A Convert within the metric system using the prefixes: kilo, hecto, deka, deci,
centi, and milli; e.g. converting millimeters to meters or liters to kiloliters. 4. A Solve real-world problems by applying these measurement formulas:
a. Perimeter of polygons using the same unit of measurement. b. Area of squares, rectangles, and triangles using the same unit of
measurement. 5. .A Identify, describe, and perform one or two transformations (reflection, rotation,
translation) on a two-dimensional figure. 6. Use all four quadrants of the coordinate plane to
a. Identify the ordered pairs of integer values on a given graph, b. Plot the ordered pairs of integer values.
7. Construct and identify 2D and 3D figures. 8. Classify polygons by sides and angles. 9. Calculate circumference and area of circles. 10. Find missing angle of a triangle. 11. Use protractor to measure, classify, and construct angles. 12. Read and interpret temperature from a thermometer. 13. Estimate the measurement of a quantity. (Job 11:9 measure)
14. ORecognize and state perimeter and area formulas for squares, rectangles, and figures derived from both.
15. OFind the volume of rectangular prisms using concrete objects. 16. OSolve real-world problems by applying measurement fmmulas for perimeter and
area.
Standard 4: Data
The student will:
1. Understand that God gave us a gift to interpret data. 2. OConstruct and interpret data using
a. Venn diagrams, b. Charts and tables, c. Frequency tables, d. Bar and circle graphs, - use church attendance and collections in weekly
bulletin to make predictions e. Pictograph, f. Line graph. g. Single stem-and-leaf plots h. Scatter plots
3. A List all possible outcomes of an experiment or simulation with a compound event composed of two independent events in a clear and organized way.
4. A Represent the probability of a simple event in an experiment or simulation using fractions and decimals.
5. ORecognize and explain the effects of scale and/or interval changes on graphs of whole number data sets.
0 Essential prerequisite skills A Assessed math indicator for KSDE
Mathematics I Grade 6 In Grade 6, instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication
and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; ( 3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
(I) Students use reasoning about multiplication and division to solve ratio and rate problems about quantities. By viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities, students connect their understanding of multiplication and division with ratios and rates. Thus students expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions. Students solve a wide variety of problems involving ratios and rates.
(2) Students use the meaning of fractions, the meanings of multiplication and division, and the relationship between mu\tipli~ cation and division to understand and explain why the procedures for dividing fractions make sense. Students use these operations to solve problems. Students extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which indudes negative rational numbers, and in particular negative integers. They reason about the order and absolute value of rational numbers and about the location of points in all four quadrants of the coordinate plane.
(3) Students understand the use of variables in mathematical expressions. They write expressions and equations that correspond to given situations, evaluate expressions, and use expressions and formulas to solve problems. Students understand that expressions in different forms can be equivalent, and they usc the properties of operations to rewrite expressions in equivalent forms. Students know that the solutions of an equation are the values of the variables that make the equation true. Students use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations. Students construct and analyze tables, such as tables of quantities that are in equivalent ratios, and they use equations (such as 3x = y) to describe relationships between quantities.
(4) Building on and reinforcing their understanding of number, students begin to develop their ability to think statistically. Students recognize that a data distribution may not have a definite center and that different ways to measure center yield different values. The median measures center in the sense that it is roughly the middle value. The mean measures center in the sense that it is the value that each data point would take on if the total of the data values were redistributed equally, and also in the sense that it is a balance point. Students recognize that a measure of variability (interquartile range or mean absolute deviation) can also be useful for summarizing data because two very different sets of data can have the same mean and median yet be distinguished by their variability. Students learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected.
Students in Grade 6 also build on their work with area in elementary school by reasoning about relationships among shapes to determine area, surface area, and volume. They find areas of right triangles, other triangles, and special quadrilaterals by decomposing these shapes, rearranging or removing pieces, and relating the shapes to rectangles. Using these methods, students discuss, develop, and justify formulas for areas of triangles and parallelograms. Students find areas of polygons and surface areas of prisms and pyramids by decomposing them into pieces whose area they can determine. They reason about right rectangular prisms with fractional side lengths to extend formulas for the volume of a right rectangular prism to fractional side lengths. They prepare for work on scale drawings and constructions in Grade 7 by drawing polygons in the coordinate plane.
Grade 6 Overview
Ratios and Proportional Relationships
• Understand ratio concepts and usc ratio reasoning to solve problems.
I . M~ke sense of problems and persevere in solving them.
The Number System
Expressions and Equations
Geometry
Statistics and Probability
• Apply and extend previous understandings of multiplitation and division to divide fractions by fractions.
• Compute fluently with multi-digit numbers and find wmmon factors and multiples.
• Apply and extend previous understandings of numbers to the system of rational numbers.
• Apply and extend previous understandings of arithmetic to algebraic expressions.
• Reason about and solve one-variable equations and inequalities.
• Represent and analyze quantitative relationships between dependent and independent variables.
• Solve real-world and mathematical problems involving area, surfate area, and volume.
• Develop understanding of statistical variability.
• Summarize and describe distributions.
2. Rea~un abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Usc appropriate tool~ strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and exprc.--.~ regularity in
repeated reasoning.
Mathematical Practices
33
Ratios and Proportional Relationships e RP
Understand ratio concepts and use ratio reasoning to solve problems.
l. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For e.wmple, "The ratio rifn·ings to beaks in the bird house at the zoo was 2:1, because for eve~v 2 wmgs there was I beak. ""For eve~y vote candidace A receh•ed, candidate C received nearly three votes."
2. Understand the concept of a unit rate afb associated with a ratio a:b with b * 0, and use rate language in the context of a ra
tio relationship. For example, "This recipe has a ratio if 3 cups if flour to 4 cups qfsugar, so there is 3;./ cup qfjlourjor each cup if sugar. ""We paid S75 for 15 hamburgers, which is a rate of$5 per hamburger." l:;
3. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in thetables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving unit pricing and constant speed. For example, !fit took 7 hours w mow 4/awns, then ac that rate, how man_,r lawns could be mowed in 35 hours? At what rate were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a guantity means 30/100 times the quantity); solve prob
lems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or
dividing quantities.
The Number System a"
Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by
using visual fraction models and equations to represent the problem. For example, create astor)' contest for (213) - (3f-t) and
use a visual fraction model to show the quotient; use che relationship between multiplication and division to erplain that (2 13) - (3 I.J) = 8f9 because 3 I .f if819 is 2f]. (In general, (u !b) - ('I d) = ad I be.) How much chocolate will each person gee
b. VVrite, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write-3 °C > -7 °( w e.~press the fact that -3 oC is warmer than -7 cC.
c. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For e.~ample,jor an account balance C?f-30 dol
lars, write 1-30 I = 30 to describe the size 1 the debt in dollars.
d. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.
8. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use
of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Expressions and Equations 6 c:E
Apply and extend previous understandings or arithmetic to algebraic expressions.
1. Write and evaluate numerical expressions involving whole-number exponents.
2. VVrite, read, and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the
calculation "Subtract y from S" asS-}'·
b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product if two factors; view (8 + 7) as both a sinale entity and a sum if two terms.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in realworld problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the
formulas V = s3 and A = 6/ to find the volume and suiface area 1 a cube with sides rif lengths = II].
3. Apply the properties of operations to generate equivalent expressions. For example, app£v the distributive propery· w the expression 3 (2 + x) to produce the equivalent e.~pression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the
equivalent expression 6 (4.t + 3;); app£v properties 1 operations toy+}'+ y to produce the equivalent expression 3y.
4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which
value is substituted into them). For e.wmple, the e.xpressions y + ,Y + y and 3.r are equivalent because they name the same number regardless 1which number y stands for.
Reason about and solve one-variable equations and inequalities.
:) . Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an
equation or inequality true.
6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in
which p, q and x are all nonnegative rational numbers.
8. VVrite an inequality of the form x > cor x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > cor x < c have infinitely many solutions; represent solutions of such ine
qualities on number line diagrams.
Represent and analy:r;e quantitative relationships between dependent and independent variables.
9. Use variables to represent tvvo quantities in a real-world problem that change in relationship to one another; vvrite an equation to express one c1uantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involvina motion at constant speed, list and graph ordered pairs 1 distances and times, and write the equation d = 6St to represent the relationshtp between distance and time.
Geometry 6G
Solve real-world and mathematical problems involving area, surface area, and volume.
1. Hnd the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical
problems.
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2. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate
unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V =I w hand V = b h to find volumes of right rectangular prisms with fractional edge lengths in
the context of solving real~world and mathematical problems.
3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side join~ ing points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real¥world and mathematical problems.
4. Represent three¥dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Statistics and Probability ,_sP ---- ------------------------------
Develop understanding of statistical variability.
1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For e:wmple, "How old am !?"is not a statistical question, but "How old are the swdenrs in m_r school?" is a statistical ques¥
tion because one anticipates rariabiliry in students' ages.
2, Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
3. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes bow its values vary with a single number.
Summarize and describe distributions.
4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
5. Summarize numerical data sets in relation to their context, such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
c. Giving quantitative measures of center (median and/ or mean) and variability (inter9uartile range and/ or mean absolute deviation), as \vel\ as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which
the data were gathered.
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