standards for mathematical practice online...

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Huntsville City Schools - Instructional Guide

2015 - 2016

Course: Math Grade: 6th Grade Honors

Standards for Mathematical Practice Online Resources The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning

Dan Meyer’s Ted Talk about teaching math: https://youtu.be/qocAoN4jNwc Links to his 3-act math activities, sorted by standard: https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0 Granite City Math Vocabulary: http://www.graniteschools.org/mathvocabulary/

For more: Other online resources Elaboration on each practice from the Common Core website: www.corestandards.org/Math/Practice/

www.opencurriculum.org is a website that curates activities from all over the web, sorted by standard.

Kid-friendly language: www.buncombe.k12.nc.us/Page/37507

http://map.mathshell.org/lessons.php has great formative assessments and group activities, also searchable by standard.

https://youtu.be/qocAoN4jNwc

https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0

https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0

http://www.graniteschools.org/mathvocabulary/

http://www.corestandards.org/Math/Practice/

http://www.opencurriculum.org/

http://www.buncombe.k12.nc.us/Page/37507

http://map.mathshell.org/lessons.php

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2015 - 2016


1st Nine Weeks

Number Systems Unit (Fractions and Decimals)

Vocabulary for Unit: numerator denominator fraction factor product cross cancel reciprocal quotient simplest form decimal divisor dividend tenths hundredths thousandths ten-thousandths

Standard

“I Can” Statements *

(to be completed by school teams)

Resources

Pacing

Recommendation / Date(s) Taught

TOPIC 5: MULTIPLYING FRACTIONS – SIXTH GRADE – 1st NINE WEEKS 7 days ALCOS #4: Interpret and compute quotients of fractions, solve word problems involving division of fractions. (6-NS1)

IXL: T.3, T.8, V.1, V.2, V.6, V.7, V.8, V.10, V.11 Digits: 5-1, 5-2, 5-3, 5-4, 5-5 AMSTI: Bits & Pieces II LTF: Area Model of Multiplication of Fractions

Recommended pacing includes teaching one lesson per day. Other days are built in for one or two pretest/review days and one test day.

TOPIC 6: DIVIDING FRACTIONS – SIXTH GRADE – 1st NINE WEEKS 7 days ALCOS #4: Interpret and compute quotients of fractions, solve word problems involving division of fractions. (6-NS1)

IXL: W.2, W.3, W.5, W.6 Digits: 6-1, 6-2, 6-3, 6-4, 6-5

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AMSTI: Bits & Pieces II: 4 Dan Meyer 3-Act Tasks: Nana’s Lemonade engageNY: Dividing Fractions Module https://www.engageny.org/resource/grade-6-mathematics-module-2

ALCOS #18: 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. (6-EE7)

Digits: 6-5 AMSTI: Shapes & Designs: 3-4 Covering & Surr.: 5

TOPIC 7: FLUENCY OF DECIMALS – SIXTH GRADE – 1st NINE WEEKS 9 days ALCOS #3(b): Solve unit rate problems including those involving unit pricing and constant speed. (6-RP3b)

IXL: G.3 Digits: 7-2, 7-3, 7-4 AMSTI: Bits & Pieces I: 3 Bits & Pieces III: 3

ALCOS #5: Fluently divide multi-digit numbers using the standard algorithm. (6-NS2)

IXL: L.1, L.2, L.5, L.6 Digits: 7-3 AMSTI: Bits & Pieces I: 3 Bits & Pieces III: 3

ALCOS #6: Fluently add, subtract, multiply, and divide multi-digit decimals using standard algorithm for each operation. (6-NS3)

IXL: J.1, J.2, O.1, O.3, O.4, 0.5, 0.6, 0.7, X.4, X.5 Digits: 7-1, 7-2, 7-4 AMSTI:

https://www.engageny.org/resource/grade-6-mathematics-module-2


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Bits & Pieces III: 1-3 ALCOS #10: Understand ordering and absolute value of rational numbers. (6-NS7)

IXL: P.21 Digits: 7-5, 7-6, 7-7

ALCOS #13(c): Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world 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). (6-EE2c)

IXL: P.1, P.2, P.4 Digits: 7-3

ALCOS #18: 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. (6-EE7)

Digits: 7-7 AMSTI: Shapes & Designs: 3-4 Covering & Surrounding: 5

Vocabulary for Unit:

area polygon plane figure square

rectangle parallelogram trapezoid pentagon

octagon formula 3-dimensional figure net

prism pyramid surface area volume

rectangular prism triangular prism triangular pyramid cube

pentagonal prism hexagonal prism octagonal prism

Geometry Unit

5

Standard

“I Can” Statements *

(to be completed by school teams)

Resources

Pacing Recommendation / Date(s) Taught

TOPIC 13: AREA – SIXTH GRADE – 1st NINE WEEKS 9 days ALCOS #13: Write, read, and evaluate expressions in which letters stand for numbers. (6-EE2)

IXL: lessons only listed for part c Digits: 13-1 AMSTI: Bits & Pieces II: 2-4 Bits & Pieces III: 1-4

ALCOS #13(c): Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world 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). (6-EE2c)

IXL: B.16, B.17, B.18 (5th grade) Digits: 13-2, 13-3, 13-4, 13-5, 13-6 AMSTI: Covering & Surrounding: 1-5

ALCOS #19: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. (6-EE8)

IXL: P.21 Digits: 13-1 AMSTI: LTF:

ALCOS #21: Find 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. (6-G1)

IXL: Z.23, Z.24 Digits:13-2, 13-3, 13-4, 13-5, 13-6 LTF: Are the Units for Area Always Square Approximating Area of Irregular Shapes Using Trapezoids

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Perimeter and Area of Triangles and Rectangles Shoeprint, Trapezoid, and Area State The Area The Biggest Area There’s a Hole in the Bucket Dear Liza, Dear Liza Dan Meyer 3-Act Tasks: Bubble Wrap

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TOPIC 14: SURFACE AREA AND VOLUME – SIXTH GRADE – 1st NINE WEEKS 9 days ALCOS #13(c): Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order. (6-EE2c)

IXL: B.23, B.25, B.26 (5th grade) Digits: 14-3, 14-4, 14-5, 14-6 engageNY: Area, Surface Area, and Volume Module https://www.engageny.org/resource/grade-6-mathematics-module-5

ALCOS #21: Find 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. (6-G1)

IXL: Z.23, Z.24, Z.26, Z.29 Digits: 14-1 AMSTI: Covering & Surrounding: 1-5

LTF: Surface Area and Volume Unit Dog

ALCOS #22: 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 = lwh and V = Bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (6-G2)

IXL: B.23, B.25 (5th grade) Z.36 (6th grade) Digits: 14-5, 14-6 AMSTI: LTF: Box It Up! Surface Area and Volume Unit Dog

ALCOS #24: 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. (6-G4)

IXL: Z.35, Z.37, Z.38 Digits: 14-2, 14-3, 14-4, 14-6 AMSTI: Covering & Surrounding: 3



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LTF: Mathematical Foundations – Nets of a Cube Unit Dog

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2015 - 2016


2nd Nine Weeks

Statistics and Probability Unit Vocabulary for Unit: statistical question data frequency dot plot intervals histogram box and whisker plot median mean mean absolute deviation range interquartile range deviation measure of center measure of variation

Standard

“I Can” Statements * (to be completed by school

teams)

Resources

Pacing


TOPIC 15: DATA DISPLAYS – SIXTH GRADE – 2nd NINE WEEKS 8 days ALCOS #9: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. (6-NS6

IXL: lessons only listed for part c Digits: 15-2, 15-3, 15-4, 15-5, 15-6

ALCOS # 9(c): Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. (6-NS6c)

IXL: B.9, C.3, Q.1, Q.2 Digits: 15-2, 15-3, 15-4, 15-5, 15-6

LTF: Alien Invasion Sketch My Graph

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ALCOS #25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (6-SP1)

IXL: S.4 Digits: 15-1 AMSTI: Data About Us: 1-3 LTF: Getting to Know You engageNY: Statistics Module https://www.engageny.org/resource/grade-6-mathematics-module-6

ALCOS #28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (6-SP4)

IXL: R.4, R.5, R.11, R.17 Digits: 15-2, 15-3, 15-4, 15-5, 15-6 AMSTI: Data About Us: 1, 3 LTF: Histograms Box and Whisker Plots

ALCOS #29: Summarize numerical data sets in relation to their context. (6-SP5)

IXL: lessons only listed for parts a, b, c Digits: 15-1, 15-2, 15-3, 15-4 AMSTI: LTF:

ALCOS #29(a): Summarize numerical data sets in relation to their context such as by: Reporting the number of observations. (6-SP5a)

IXL: R.6 Digits: NONE AMSTI: How Likely Is It?: 1-4



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LTF: Histograms

ALCOS # 29(b): Summarize numerical data sets in relation to their context such as by: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. (6-SP5b)

IXL: S.4 Digits: 15-1 AMSTI: Data About Us: 1-2

ALCOS # 29(c): Summarize numerical data sets in relation to their context, such as by: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation) as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (6-SP5c)

IXL: S.2, S.2, S.3 Digits: 15-2, 15-3, 15-4 AMSTI: Data About Us: 1-2

LTF: Getting to Know You

TOPIC 16: MEASURES OF CENTER AND VARIATION – SIXTH GRADE – 2nd NINE WEEKS 8 days ALCOS #26: 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. (6-SP2)

Digits: 16-3 AMSTI: Data About Us: 1-3 LTF: Home Runs, Statistics, and Probability

ALCOS #27: 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 how its values vary with a single number. (6-SP3)

Digits: 16-1, 16-2, 16-3, 16-4, 16-5, 16-6 AMSTI: Data About Us: 1-3 LTF: Home Runs, Statistics, and Probability

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ALCOS #28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. (6-SP4)

IXL: R.4, R.5, R.11, R.17 Digits: 16-1 AMSTI: Data About Us: 1, 3 LTF: Box and Whisker Plots Histograms Home Runs, Statistics, and Probability

ALCOS #29: Summarize numerical data sets in relation to their context. (6-SP5)

Digits: 16-2, 16-4, 16-5

ALCOS #29(c): Summarize numerical data sets in relation to their context, such as by: Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation) as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. (6-SP5c)

IXL: lessons only listed for part c Digits: 16-2, 16-4, 16-5 AMSTI: Data About Us: 1-3 LTF: Home Runs, Statistics, and Probability

ALCOS #29(d): Summarize numerical data sets in relation to their context, such as by: 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. (6-SP5d)

Digits: NONE AMSTI: Data About Us: 3 LTF: Box and Whisker Plots Histograms Counting Ursus Actos Horribilis, the Grizzly Bear Home Runs, Statistics, and Probability Measures of Central Tendency and Variability

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RATIO AND PROPORTIONAL RELATIONSHIPS UNIT Vocabulary for Unit:

ratio rate unit rate percent

proportions equivalent fractions equivalent ratios terms of a ratio

unit price least common multiple constant of proportionality dependent variable

independent variable scale drawing scale percent equation

commission interest simple interest principal

interest rate balance interest period markup

markdown percent of increase percent of decrease dimensional analysis

Standard


teams)

Resources

Pacing


TOPIC 1: RATIOS AND RATES – SEVENTH GRADE – 2nd NINE WEEKS 7 days ALCOS #1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. (7-RP1)

IXL: J.1, J.5, L.3, L.4 Digits: 1-1, 1-2, 1-3, 1-4, 1-5 AMSTI: Bits and Pieces 1: 3-4, Comparing and Scaling: 3 Stretching and Shrinking: 1-5

LTF: Calculating Hurricane Lili’s Wind Speed Fire Trucks, Sky Divers, and Softball Metric and Customary Measurements

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Rate Graphs Rating the Trip Walk the Line Dan Meyer 3-Act Tasks: Graduation

TOPIC 2: PROPORTIONAL RELATIONSHIPS – SEVENTH GRADE – 2nd NINE WEEKS 8 days ALCOS #2: Recognize and represent proportional relationships between quantities. (7-RP2)

IXL: lessons only listed for parts a, b, c Digits: 2-1, 2-3, 2-4, 2-6 AMSTI: Comparing and Scaling: 1-4 Stretching and Shrinking: 1-4 Filling and Wrapping: 5 How Likely is it?: 1-4 What Do You Expect?: 1-4 LTF: Average Rate of Change Match My Run Road Trip Dan Meyer 3-Act Tasks: Final’s Week

ALCOS #2(a): Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. (7-RP2a)

IXL: J.2, J.3, J.6, J.7, X.1 Digits: 2-1, 2-2 AMSTI: Comparing and Scaling: 1-4 Stretching and Shrinking: 1-4 Filling and Wrapping: 5 How Likely is it?: 1-4 What Do You Expect?: 1-4

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ALCOS #2(b): Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (7-RP2b)

IXL: X.2 Digits: 2-3, 2-4 AMSTI: Comparing and Scaling: 1-4 Stretching and Shrinking: 1-4 Filling and Wrapping: 5 How Likely is it?: 1-4 What Do You Expect?: 1-4 LTF: Interpreting Distance Graphs Interpreting Rate Graphs

ALCOS #2(c): Represent proportional relationships by equations. (7-RP2c)

IXL: J.8, J.9, I.5 (8th) Digits: 2-4 AMSTI: Comparing and Scaling: 1-4 Stretching and Shrinking: 1-4 Filling and Wrapping: 5 How Likely is it?: 1-4 What Do You Expect?: 1-4

ALCOS #2(d): Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. (7-RP2d)

Digits: 2-5 , 2-6 AMSTI: Comparing and Scaling: 1-4 Stretching and Shrinking: 1-4 Filling and Wrapping: 5 How Likely is it?: 1-4 What Do You Expect?: 1-4

ALCOS #11: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (7-G1)

IXL: J.13, P.12, P.13, P.14, P.15, P.16, P.30 Digits: 2-5 , 2-6, AMSTI: Comparing and Scaling: 1-4

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Stretching and Shrinking: 1-4 Filling and Wrapping: 5 How Likely is it?: 1-4 What Do You Expect?: 1-4 LTF: New Home for Rami, the Unwanted Rhinoceroses engageNY: Ratios of Scale Drawings Module https://www.engageny.org/resource/grade-7-mathematics-module-1-topic-d-overview

TOPIC 3: PERCENTS – SEVENTH GRADE – 2nd NINE WEEKS 9 days ALCOS #2: Recognize and represent proportional relationships between quantities. (7-RP2)

IXL: lessons only listed for parts b, c Digits: 3-1, 3-2, 3-3, 3-4, 3-5 AMSTI: Comparing and Scaling: 1-4 Stretching and Shrinking: 1-4 Filling and Wrapping: 5 How Likely is it?: 1-4 What Do You Expect?: 1-4

https://www.engageny.org/resource/grade-7-mathematics-module-1-topic-d-overview

https://www.engageny.org/resource/grade-7-mathematics-module-1-topic-d-overview

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ALCOS #2(b): Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. (7-RP2b)

IXL: X.2 Digits: 3-1 AMSTI: Bits and Pieces III: 4-5 Variables and Patterns: 4 Comparing and Scaling: 1-4 Stretching and Shrinking: 4-5 Growing, Growing, Growing: 4

ALCOS #2(c): Represent proportional relationships by equations. ( 7-RP2c)

IXL: J.8, J.9, I.5 (8th) Digits: 3-1 AMSTI: Bits and Pieces III: 4-5 Variables and Patterns: 4 Comparing and Scaling: 1-4 Stretching and Shrinking: 4-5 Growing, Growing, Growing: 4

ALCOS #3: Use proportional relationships to solve multistep ratio and percent problems. (7-RP3)

IXL: K.4, K.7, K.8, K.9, K.10, L.6, L.7, L.9, L.10, L.11 Digits: 3-2, 3-3, 3-4, 3-5, 3-6, 3-7 AMSTI: Bits and Pieces III: 4-5 Variables and Patterns: 4 Comparing and Scaling: 1-4 Stretching and Shrinking: 4-5 Growing, Growing, Growing: 4 Dan Meyer 3-Act Tasks: Dueling Discounts

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Huntsville City Schools - Instructional Guide 2015 - 2016


3rd Nine Weeks

RATIONAL NUMBERS UNIT

Vocabulary for Unit:

absolute value integers rational numbers whole numbers

additive inverses reciprocals complex fractions repeating decimals

terminating decimals accuracy percent error

Standard


teams)

Resources

Pacing


TOPIC 4: ADDING AND SUBTRACTING RATIONAL NUMBERS – SEVENTH GRADE 9 days

3rd NINE WEEKS ALCOS #4: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. (7-NS1)

IXL: E.3, E.4, E.5 Digits: 4-1, 4-2, 4-3, 4-4, 4-5, 4-7 AMSTI: Accentuate the Negative: 2, 3 Bits and Pieces II: 1-2 Bits and Pieces III: 1 Accentuate the Negative: 2, 4 engageNY: Rational Numbers Module https://www.engageny.org/resource/grade-7-mathematics-module-2



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ALCOS #4(a): Describe situations in which opposite quantities combine to make 0. (7-NS1a)

IXL: D.3 Digits: 4-1 AMSTI: Accentuate the Negative: 2, 3 Bits and Pieces II: 1-2 Bits and Pieces III: 1 Accentuate the Negative: 2, 4

ALCOS #4(b): Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. (7-NS1b)

IXL: B.3, D.2, D.3, D.5 Digits: 4-2, 4-3, 4-5 AMSTI: Accentuate the Negative: 2, 3 Bits and Pieces II: 1-2 Bits and Pieces III: 1 Accentuate the Negative: 2, 4

ALCOS #4(c): Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. (7-NS1c)

IXL: E.1, E.3, E.4, E.5, H.6 Digits: 4-4, 4-6, 4-7 AMSTI: Accentuate the Negative: 2, 3 Bits and Pieces II: 1-2 Bits and Pieces III: 1 Accentuate the Negative: 2, 4

ALCOS #4(d): Apply properties of operations as strategies to add and subtract rational numbers. (7-NS1d)

IXL: C.1, C.11, E.9, G.1, G.3, Y.1 Digits: 4-3 AMSTI: Accentuate the Negative: 2, 3 Bits and Pieces II: 1-2 Bits and Pieces III: 1 Accentuate the Negative: 2, 4

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ALCOS #9: Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. (7-EE3)

IXL: B.4, C.7, C.9, C.10, C.11, E.9, F.1, F.2, F.5, F.6, F.7, F.8, F.9, G.6, G.14, G.16, Digits: 4-1, 4-7

TOPIC 5: MULTIPLYING AND DIVIDING RATIONAL NUMBERS – SEVENTH GRADE 8 days

3rd NINE WEEKS ALCOS #5: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. (7-NS2)

IXL: lessons only listed for parts a, b, c Digits: 5-1, 5-2, 5-3, 5-4, 5-5 AMSTI: Accentuate the Negative: 1-4 Bits and Pieces II: 3 Bits and Pieces III: 2 Comparing and Scaling: 3 Variables and Patterns: 2-4 Looking for Pythagoras: 3-4

ALCOS #5(a): Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. (7-NS2a)

IXL: E.6, E.7, E.8, H.7, Y.2 Digits: 5-1, 5-2 AMSTI: Accentuate the Negative: 1-4 Bits and Pieces II: 3 Bits and Pieces III: 2 Comparing and Scaling: 3 Variables and Patterns: 2-4 Looking for Pythagoras: 3-4

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ALCOS #5(b): Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then - (p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. (7-NS2b)

IXL: A.3, A.4, C.6, E.6, E.7, E.8, Digits: 5-3, 5-4, 5-5 AMSTI: Accentuate the Negative: 1-4 Bits and Pieces II: 3 Bits and Pieces III: 2 Comparing and Scaling: 3 Variables and Patterns: 2-4 Looking for Pythagoras: 3-4

ALCOS #5(c): Apply properties of operations as strategies to multiply and divide rational numbers. (7-NS2c)

IXL: C.3, C.5, C.11, E.9, G.7, G.8, G.9, G.11, G.12, Y.1 Digits: 5-1 AMSTI: Accentuate the Negative: 1-4 Bits and Pieces II: 3 Bits and Pieces III: 2 Comparing and Scaling: 3 Variables and Patterns: 2-4 Looking for Pythagoras: 3-4

ALCOS #6: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) (7-NS3)

IXL: C.1, C.2, C.3, C.4, C.5, C.6, C.7, C.8, E.3, E.4, E.5, E.6, E.7, E.8, G.1, G.2, G.3, G.4, G.5, G.7, G.8, G.9, g.10, G.11, G.12, G.13, G.15, H.6, H.7, L.1, L.2 Digits: 5-5, 5-6 AMSTI: Accentuate the Negative: 1-4 Bits and Pieces II: 3 Bits and Pieces III: 2 Comparing and Scaling: 3 Variables and Patterns: 2-4 Looking for Pythagoras: 3-4

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IXL: M.1, M.2, M.3, M.6 Digits: 5-6 AMSTI: Accentuate the Negative: 1-4 Bits and Pieces II: 3 Bits and Pieces III: 2 Comparing and Scaling: 3 Variables and Patterns: 2-4 Looking for Pythagoras: 3-4 LTF: Arithmetic Sequences

TOPIC 6: DECIMALS AND PERCENTS – SEVENTH GRADE – 3rd NINE WEEKS 8 days ALCOS #3: Use proportional relationship to solve multistep ratio and percent problems. (7-RP3)

IXL: L.4, L.5, L.6, L.7, L.8, L.9, L.10, L.11 Digits: 6-6 Dan Meyer 3-Act Tasks: Dueling Discounts

ALCOS #5(b): Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with nonzero divisor) is a rational number. If p and q are integers, then - (p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts. (7-NS2b)

IXL: C.6 Digits: 6-1, 6-2, 6-5 AMSTI: Accentuate the Negative: 2-4 Comparing and Scaling: 3

ALCOS #5(d): Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. (7-NS2d)

IXL: A.10, H.2 Digits: 6-1, 6-2, 6-5 AMSTI: Accentuate the Negative: 2-4 Comparing and Scaling: 3

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ALCOS #6: Solve real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.) (7-NS3)

IXL: C.3, C.4, C.5, C.6, C.8 Digits: 6-3, 6-4, 6-5, 6-7 AMSTI: Accentuate the Negative: 2-4 Comparing and Scaling: 3

Expressions and Equations Unit Vocabulary for Unit:

expression numerical expression operations order of operations

variable algebraic expression evaluate exponent

term coefficient product factor

formula greatest common factor multiple least common multiple

distributive property substitution equivalent inequality

quadrant coordinate plane like terms coefficients

constants simplify expand factor

equation isolate two-step equation inequality

solution set conjecture equivalent inequalities

Standard


teams)

Resources

Pacing


TOPIC 7: EQUIVALENT EXPRESSIONS – SEVENTH GRADE – 3rd NINE WEEKS 7 days ALCOS #7: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. (7-EE1)

IXL: U.6, Y.1, Y.2, Y.3 Digits: 7-1, 7-2, 7-3, 7-4, 7-5 AMSTI: Thinking With Mathematical Models: 2-3 Growing, Growing, Growing: 1

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Frogs, Fleas, and Painted Cubes: 2 Say it With Symbols: 1-4 Shapes of Algebra: 2-5 engageNY: Expressions and Equations Module https://www.engageny.org/resource/grade-7-mathematics-module-3

ALCOS #8: Understand that rewriting an expression in different forms in a problem context can shed light on the problem, and how the quantities in it are related. Understand that rewriting an expression in different forms in a problem context can shed light on the problem, and how the quantities in it are related. (7-EE2)

Digits: 7-1, 7-2, 7-3, 7-4, 7-5

TOPIC 8: EQUATIONS – SEVENTH GRADE – 3rd NINE WEEKS 8 days ALCOS #9: Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. (7-EE3)

Digits: 8-3, 8-4, 8-5 AMSTI: Variables and Patterns: 1-3 Moving Straight Ahead: 1-4 Thinking With Mathematical Models: 1-3 Looking for Pythagoras: 3-4 Growing, Growing, Growing,: 1-4 Frogs, Fleas, and Painted Cubes: 1-4 The Shapes of Algebra: 2-5 Say it with Symbols: 1-5

ALCOS #10: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. (7-EE4)

IXL: J.9, V.2, V.3, V.4, V.5, X.10, Y.4 Digits: 8-1, 8-2, 8-3, 8-4, 8-5 AMSTI: Variables and Patterns: 1-3 Moving Straight Ahead: 1-4 Thinking With Mathematical Models: 1-3 Looking for Pythagoras: 3-4



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Growing, Growing, Growing,: 1-4 Frogs, Fleas, and Painted Cubes: 1-4 The Shapes of Algebra: 2-5 Say it with Symbols: 1-5

ALCOS #10(a): Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (7-EE4a)

IXL: V.3, V.4, V.5 Digits: 8-1, 8-2, 8-3, 8-4, 8-5 AMSTI: Variables and Patterns: 1-3 Moving Straight Ahead: 1-4 Thinking With Mathematical Models: 1-3 Looking for Pythagoras: 3-4 Growing, Growing, Growing,: 1-4 Frogs, Fleas, & Painted Cubes: 1-4 The Shapes of Algebra: 2-5 Say it with Symbols: 1-5

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2015 - 2016


4th Nine Weeks

TOPIC 9: INEQUALITIES – SEVENTH GRADE – 4th NINE WEEKS 9 days ALCOS #10: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. (7-EE4)

IXL: W.1, W.2, W.3, W.4, W.5, W.6, W.7 Digits: 9-1, 9-2, 9-3, 9-4, 9-5 AMSTI: Variables and Patterns: 1-3 Moving Straight Ahead: 1-4 Looking for Pythagoras: 3-4 Growing, Growing, Growing,: 1-4 Frogs, Fleas, & Painted Cubes: 1-4 The Shapes of Algebra: 2-5 Say It With Symbols: 1-5

ALCOS #10(b): Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality, and interpret it in the context of the problem. (7-EE4b)

IXL: W.1, W.2, W.3, W.4, W.5, W.6, W.7 Digits: 9-1, 9-2, 9-3, 9-4, 9-5 AMSTI: Variables and Patterns: 1-3 Moving Straight Ahead: 1-4 Looking for Pythagoras: 3-4 Growing, Growing, Growing,: 1-4 Frogs, Fleas, & Painted Cubes: 1-4 The Shapes of Algebra: 2-5

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Say It With Symbols: 1-5

Geometry Unit Vocabulary for Unit:

angle vertex straight angle obtuse angle acute angle right angle adjacent angles complementary angles supplementary angles vertical angles circle center of a circle radius diameter circumference area

Standard


teams)

Resources

Pacing


TOPIC 10: ANGLES – SEVENTH GRADE – 4th NINE WEEKS 10 days ALCOS #10: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. (7-EE4)

IXL: V.3, V.4, V.5 Digits: 10-1, 10-2, 10-3, 10-4, 10-5, 10-6 AMSTI: Variables and Patterns: 1-3 Moving Straight Ahead: 1-4 Looking for Pythagoras: 3-4 Growing, Growing, Growing,: 1-4 Frogs, Fleas, and Painted Cubes: 1-4 The Shapes of Algebra: 2-5 Say It With Symbols: 1-5

ALCOS #10(a): Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence

IXL: J.9, X.10 Digits: 10-1, 10-2, 10-3, 10-4, 10-5, 10-6 AMSTI:

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of the operations used in each approach. (7-EE4a)

Variables and Patterns: 1-3 Moving Straight Ahead: 1-2 Say It With Symbols: 1-5 Thinking With Mathematical Models: 1-3 Shapes and Designs: 4 Filling and Wrapping: 1-4 Stretching and Shrinking: 3 LTF: Angles of a Regular Polygon

ALCOS #12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. (7-G2)

Digits: 10-1, 10-2, 10-3, 10-4, 10-5 AMSTI: Variables and Patterns: 1-3 Moving Straight Ahead: 1-4 Looking for Pythagoras: 3-4 Growing, Growing, Growing,: 1-4 Frogs, Fleas, & Painted Cubes: 1-4 The Shapes of Algebra: 2-5 Say It With Symbols: 1-5

ALCOS #15: Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure. (7-G5)

IXL: P.4, P.5 Digits: 10-2, 10-3, 10-4, 10-5, 10-6 AMSTI: Variables and Patterns: 1-3 Moving Straight Ahead: 1-4 Looking for Pythagoras: 3-4 Growing, Growing, Growing,: 1-4 Frogs, Fleas, & Painted Cubes: 1-4 The Shapes of Algebra: 2-5 Say It With Symbols: 1-5 LTF: Angles of a Regular Polygon

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TOPIC 11: CIRCLES – 4th NINE WEEKS 10 days ALCOS #9: Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. (7-EE3)

IXL: M.2, M.3 Digits: 11-3 , 11-4, 11-5 AMSTI: Covering and Surrounding: 5 Filling and Wrapping: 2-5

ALCOS #10: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. (7-EE4)

IXL: V.3, V.4, V.5 Digits: 11-1, 11-2, 11-3, 11-4, 11-5 AMSTI: Covering and Surrounding: 5 Filling and Wrapping: 2-5

ALCOS #10(a): Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (7-EE4a)

IXL: V.3, V.4, V.5 Digits: 11-1 AMSTI: Covering and Surrounding: 5 Filling and Wrapping: 2-5 LTF: Discovering Area

ALCOS #14: Know the formulas for the area and circumference of a circle, and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. (7-G4)

IXL: P.21, P.22, P.23 Digits: 11-1, 11-2, 11-3, 11-4, 11-5

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AMSTI: Covering and Surrounding: 5 Filling and Wrapping: 2-5 LTF: An ‘Apeeling’ Problem Discovering Area Finding Pi Working with Formulas Dan Meyer 3-Act Tasks: Penny Circle Coffees Traveler Popcorn Picker

ALCOS #12: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. (7-G2)

Digits: 11-1, 11-2, 11-3 AMSTI: Covering and Surrounding: 5 Filling and Wrapping: 2-5

Probability Unit – Seventh Grade

Vocabulary for Unit: probability of an event outcome sample space event action trial relative frequency experimental probability theoretical probability simulation probability model uniform probability model

Standard


teams)

Resources

Pacing


TOPIC 16: PROBABILITY CONCEPTS – SEVENTH GRADE – 4th NINE WEEKS 10 days ALCOS #4(c): Understand subtraction of rational numbers as adding the additive

IXL:D.2, E.1, E.3, E.4, E.5, H.6

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inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. (7-NS1c)

Digits: 16-4


IXL: C.9, M.2 Digits: 16-1, 16-3, 16-4, 16-5, 16-6

ALCOS #21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. (7-SP5)

IXL: Z.1 Digits: 16-1 AMSTI: How Likely Is It?: 1-4 What Do You Expect?: 1-4 LTF: Bulls Eye

ALCOS #22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. (7-SP6)

IXL: Z.3, Z.4 Digits: 16-1, 16-3 LTF: Free French Fries Passing Game Using Area to Estimate Probability

ALCOS #23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good,

IXL: lessons only listed for parts a, b Digits: 16-2, 16-4, 16-5, 16-6

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explain possible sources of the discrepancy. (7-SP7)

ALCOS #23(a): Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. (7-SP7a)

IXL: Z.1 Digits: 16-5, 16-6

ALCOS #23(b): Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. (7-SP7b)

IXL: Z.3 Digits: 16-6

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Sixth Grade Standards covered by a seventh grade digits

lesson, not a sixth grade digits lesson. (These lessons are listed in the Sixth Grade Honors Math Pacing Guide and

do not need to be taught separately. This listing is for reference only.)

Standard


teams)

Resources

Pacing


ALCOS #1: Understand the concept of a ratio, and use ratio language to describe a ratio relationship between two quantities. (6-RP1)

Digits: Seventh Grade 1-1

ALCOS #2: Understand the concept of a unit rate a/b associated with a ratio a: b with b ≠ 0, and use rate language in the context of a ratio relationship. (6-RP2)


ALCOS #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. (6-RP3)


ALCOS #3(a): Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. (6-RP3a)


ALCOS #3(c): Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. (6-RP3c)


ALCOS #8: Understand that positive and negative numbers are used together to


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describe quantities having opposite directions or values. (e.g. temperature; elevation; credits/debits; positive/negative electrical charge); use positive and negative numbers to represent quantities in real-world contexts explaining the meaning of 0 in each situation. (6-NS5)

ALCOS #9(a): Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., – (–3) = 3, and that 0 is its own opposite. (6-NS6a) ALCOS #9(a): Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., – (–3) = 3, and that 0 is its own opposite. (6-NS6a)


ALCOS #9(b): Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. (6-NS6b)


ALCOS #10(a): Interpret statements of inequality as statements about the relative position of two numbers on a number line. (6-NS7a)


ALCOS #10(b): Write, interpret, and explain statements of order for rational numbers in real-world contexts. (6-NS7b)


ALCOS #10(c): Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as


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magnitude for a positive or negative quantity in a real-world situation. (6-NS7c) ALCOS #10(d): Distinguish comparisons of absolute value from statements about order. (6-NS7d)


ALCOS #11: 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. (6-NS8)


ALCOS #13(a): Write expressions that record operations with numbers and with letters

standing for numbers. (6-EE2a)


ALCOS #13(b): Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, and coefficient); view one of more parts of an expression as a single entity. (6-EE2b)


ALCOS #14: Apply the properties of operations to generate equivalent expressions. (6-EE3)


ALCOS #15: Identify when two expressions are equivalent (i.e. when the two expressions name the same number regardless of which value is substituted into them). (6-EE4)


ALCOS #16: 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-EE5)

Digits: Seventh Grade 8-1, 9-1, 9-2

ALCOS #17: Use variables to represent numbers, and write expressions when solving


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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. (6-EE6)

ALCOS #20: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, 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 the independent variables using graphs and tables, and relate these to the equation. (6-EE9)


standards for mathematical practice online...

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