grade 6 overview

BPS Mathematics Department G6 Updated: 12/15/2020

Instructional Guide Grade 6 – Mathematics

February 2021 through June 2021

Grade 6 Overview

Module Standards

M1: Ratios and Unit Rates 6.RP.1, 6.RP.2, 6.RP.3

M2: Arithmetic Operations Including Dividing by a Fraction 6.NS.1, 6.NS.2F, 6.NS.3F, 6.NS.4 F = Required Fluency for Grade 6

M3: Rational Numbers 6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8

M4: Expressions and Equations 6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4, 6.EE.5, 6.EE.6,

6.EE.7, 6.EE.8, 6.EE.9

M5: Area, Surface Area, and Volume Problems 6.G.1, 6.G.2, 6.G.3, 6.G.4

M6: Statistics

Gr. 7 M5: Various Lessons

6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5,

7.SP.1, 7.SP.2, 7.SP.5, 7.SP.6, 7.SP.7

See PAGE 7 for your February to June PACING




IMPORTANT Module 3 Notes:

Based on the Next Generation Math Standards (to be implemented YEAR NEXT), please keep the following upcoming changes in mind, as you teach this Module:

● 6.NS.6 Clarification in the wording of the standard to include “Use number lines and coordinate axes to represent points on a number line and in the coordinate plane with negative number coordinates.”

● 6.NS.7d Clarification in the wording of the standard to include a new example “Someone with a balance of $100 in their bank account has more money than someone with a balance of -$1,000, because 100 > -1,000. But the second person’s debt is much larger than the first person’s credit because |-1,000| > |100|.”

● 6.NS.8 Clarification in the wording of the standard from “in all four quadrants” to “on a coordinate plane”

Module 3 Vocabulary

Absolute Value Charge Credit Debit

Elevation Integers Magnitude Negative Number

Opposite Positive Number Quadrants Rational Number

Rational Number Withdraw




IMPORTANT Module 4 Notes: Based on the Next Generation Math Standards (to be implemented YEAR NEXT), please keep the following upcoming changes in mind, as you teach this Module:

● 6.EE.7 Clarification in the wording of the standard to include “x – p =q” “x/p =q”. All four single-step equations are now included.

● 6.EE.8 Clarification in the wording of the standard to include “x ≤ c, x ≥ c” Compound inequalities could be introduced here.

● 6.EE.9 Clarification in the wording of the standard “write an equation” is replaced with “given an equation” to limit the scope of the standard and allow focus on the importance of identifying dependent and independent variable given a particular real-world situation.

Module 4 Vocabulary

Coefficient Equation Equivalent Expressions Exponential Notation for

Whole Number Exponents

Inequality Linear Expression Order Of Operations Simple Expression

Term Truth Values of a Number

Sentence





● 6.G.1 Clarification in the wording of the standard to “Find are of triangles, trapezoids, and other polygons by composing into rectangles or decomposing into triangles and quadrilaterals. Apply these techniques in the context of solving real-world and mathematical problems. Note: The inclusive definition of trapezoid will be utilized, which defines a trapezoid as “A quadrilateral with at least one pair of parallel sides.” (This definition include a parallelogram).”

● 6.G.2 Clarification in the wording of the standard to “Find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems”

● 6.G.4 Clarification in the wording of the standard to include “Note: Three-dimensional figures include only right rectangular prisms, right rectangular pyramids, and right triangular prisms. When finding surface areas, all necessary measurements will be given.”

● Added Standard: 6.G.5 Use area and volume models to explain perfect squares and perfect cubes.

Module 5 Vocabulary

Altitude of a Triangle Area Area of a Rectangle Area of a Triangle

Base Cube Hexagon Net

Parallel Planes Pentagon Perpendicular Plane Polygons

Prism Right Rectangular Prism Surface Area Surface of a Prism

Triangular Region Vertex (Vertices) Volume





● Added Standard: 6.SP.1b Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Note: Students need to understand that data are generated with respect to particular contexts or situations and can be used to answer questions about those contexts or situations. (Currently in G7 M5 Topic C)

● Added Standard: 6.SP.1c Understand that the method and sample size used to collect data for a particular question is intended to reduce the difference between a population and a sample taken from the population so valid inferences can be drawn about the population. Generate multiple samples (or simulated samples) of the same size to recognize the variation in estimates or predictions. Note: Examples of acceptable methods to obtain a representative sample from a population include, but are not limited to, a simple random sample for a given population or a systematic random sample for an unknown population. Examples of unacceptable methods of sampling include, but are not limited to, online polls and convenience sampling because they introduce bias and are not representative of the population. (Currently in G7 M5 Topic C)

● 6.SP.2 Clarification in the wording of the standard to include “Notes: Students need to determine and justify the most appropriate graph to display a given set of data (histogram, dot plot). Students extend their knowledge of symmetric shapes, to describe data displayed in dot plots and histograms in terms of symmetry. They identify clusters, peaks and gaps, recognizing common shapes and patterns in these displays of data distributions, and ask why a distribution takes on a particular shape for the context of the variable being considered.”

● 6.SP.3 Clarification in the wording of the standard to include “Note: Measures of center are mean, median, and mode. The measure of variation is the range.”

● 6.SP.4 and 6.SP.5 Clarification in the wording of the standard from “numerical” to “quantitative”. ● 6.SP.5c Change in the wording of the standard to “Calculate range and measures of center, as well as describe any overall

pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. Note:




Measures of center are mean, median, and mode. The measure of variation is the range. Role of outliers should be discussed, but no formula required.”

● 6.SP.5d Clarification in the wording of the standard to include “the range” and “Note: Measure of center are mean, median, and mode. The measure of variation is the range.”

● Added Standard: 6.SP.6 Understand that the probability of a chance event is a number between 0 and 1 inclusive, 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. (Currently in G7 M5 Lesson 1)

● Added Standard: 6.SP.7 Approximate the probability of a simple 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. e.g., When rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times. Note: Compound events are introduced in grade 7. (Currently in G7 M5 Topic A, Lessons 8 and 12)

● Added Standard: 6.SP.8 Develop a probability model and use it to find probabilities of simple events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. (G7 M5 Lesson 4)

● Added Standard: 6.SP.8a Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of simple events. e.g., The probability of rolling a six-sided fair number cube and landing on a 2

is 𝟏/ . The probability of landing on an even number is 𝟑/𝟔. (G7 M5 Lesson 4) ● Standard: 6.SP.8b Develop a probability model (which may not be uniform) by observing frequencies in data generated from a

chance process. e.g., Find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies? (G7 M5 Lessons 5, 8, 9 and 12)

Module 6 Vocabulary

Box Plot Dot Plot Histogram

Line Plot Mean Mean Absolute Deviation (MAD)

Median Statistical Question Variability Deviations from the

Mean




PACING Plan for February 2021 – June 2021

Please note that there will be times throughout the YEAR when you will either be embedding lessons from the previous grade level, omitting lessons at this grade level, and/or combining lessons at this grade level. This is all to ensure that our students have the foundational and grade level conceptual understanding to

progress masterfully as the standards outline.

The decisions that were made were based on the progression of content from grade to grade (coherence). Those March - June standards that underline the mastery of this year's standards were deemed essential

and it was determined that they must be embedded in this years' pacing.

Grade 6

Quarter 3 - weeks Quarter 3 - dates Feb - June PACING

Zearn Digital Independent

Lessons NOTE – Zearn’s Grade 6 Missions are not in the same order as the Math

Modules.

Instructional Notes

Note: In order to ensure that all test content is covered prior to the NYS math assessment, the number of synchronous lessons during a couple of the Quarter 3 weeks will be increased to 4. The weeks during which there are 4 lessons are also the weeks for which there are no parallel Zearn lessons.

Week 21 2/1-2/5 M4: Lessons 1/2, 3/4, 5

Mission 6 Lesson 12 to support Module Lesson 5

Combine Lessons 1 and 2, they have the same objective/cover the same concept, relationships of operations. Combine the problem sets and exit tickets. Combine Lessons 3 and 4, they have the same objective/cover the same concept, relationships of operations. Combine the problem sets and exit tickets.




Week 22 2/8-2/12 M4: Lesson 6, 7, 8

Mission 6 Lesson 14 to support Module Lesson 6

Week 23 2/22-2/26 M4: Lesson 9, 10, 11

Mission 6 Lesson 6 to support Module Lesson 9 and review Lesson 8

Week 24 3/1-3/5 M4: Lesson 12, 13/14, 15, 16/17 (4 synchronous days)

Mission 6 Lessons 9 or 10 to support Lesson 12 *look at these lessons and choose the one that best meets your student’s needs

Combine Lessons 13/14, they have the same objective/cover the same concept, writing division expressions. Use examples from both lessons, omit Lesson 13 exercises as they are similar to Lesson 14 exercise. Combine exit tickets. Combine Lessons 16/17, they have the same objective/cover the same concept, write expressions in which letters stand for numbers. Use the opening and mathematical modeling exercises in Lesson 16 and the station activity exercise from Lesson 17. Combine the exit tickets.

Week 25 3/8-3/12 M4: Lesson 18/19 and 20/21/22

Mission 6 Lesson 16 to support Lesson 20

Combine Lessons 18/19, they have the same objective/cover the same concept, writing and evaluating expressions. In Lesson 18, omit exercise 1-2, but focus on descriptions in example 2. Combine problem sets and exit tickets. Combine Lessons 20/21/22, they have the same objective/cover the same concept, writing and evaluating expressions. Use 2 days to complete these 3 lessons.

Week 26 3/15-3/18 M4: Lesson 23/24, 25, 26/27

Mission 6 Lesson 1 to support Lessons 25-27

Combine Lessons 23/24, they have the same objective/cover the same concept, true and false number sentences. Omit L24 opening exercise as it is a review of L23. Combine problem sets and exit tickets. Combine Lessons 26/27, they have the same




objective/cover the same concept, one step equations using a tape diagram. In Lesson 27 omit the exploratory challenge. Combine the problem sets and exit tickets.

Week 27 3/22-3/26 M4: Lesson 28/29, 30, 31/32, 33 (4 synchronous days)

Combine Lessons 28/29, they have the same objective/ cover the same concept, calculating solutions to two- and multi-step equations. Combine problem sets and exit tickets. Combine Lessons 31/32, they have the same objective/cover the same concept, choosing independent and dependent variables, creating tables and graphs for an equation. Omit Lesson 31 problem set and exit ticket.

Week 28 Fri No School

3/29-4/2 M4: Lesson 34 M5: Lesson 1

Mission 7 Lesson 9 to support Lessons 34 and review Lesson 33. Mission 5 Lesson 6 to support Lesson 1 *Mission 6 Lesson 5 can be used if students require additional support identifying the height and base of a parallelogram




Week 29 4/12-4/16 M5: Lesson 2/3/4, 5/6, 7

Mission 1 Lesson 9 or 10 to support Lessons 2-4 *look at these lessons and choose the one that best meets your student’s needs Mission 1 Lesson 3 to support Lesson 5-6 *Mission 1 Lesson 2 can be used if students require additional support decomposing figures

Combine Lessons 2/3/4, they have the same objective/cover the same concept, area of triangles. In Lesson 2 omit the exploratory challenge, instead show how the area formula is derived using a rectangle. Use area formula in lesson 3 and 4. Combine problem sets and exit tickets. Combine Lessons 5/6, they have the same objective/cover the same concept, finding area by composition and decomposition of polygons. Omit Lesson 6 exploratory challenges, combine the problem sets and exit tickets.

Week 30 Tues & Wed Testing

4/19-4/23 M5: Lesson 8/9, 11/12 Mission 1 Lesson 11 to support Lesson 8 *Note this lesson does not include writing expressions or explaining *Zearn does not have any Grade 6 Missions that parallel Grade 6 volume content. However, Zearn does have Grade 5 Missions that are an introduction to volume (Grade 5 Mission 5 Lessons 1-3) AND Missions that are real world applications of volume (Grade 5 Mission 5 Lessons 5 and 7).

- You may want to take a look at to see if they meet your student’s needs for review.

Combine Lessons 8/9, they have the same objective/ cover the same concept, using the coordinate plane and different methods to solve for the area and perimeter of a polygon. Combine the problem sets and exit tickets. Omit Lesson 10, use the problem set and exit ticket problems with Lessons 8 and 9. Combine Lessons 11/12, they have the same objective/cover the same concept, using unit cubes and formula to determine volume of a prism. Combine the problem sets and exit tickets.




Quarter 4 - weeks Quarter 4 - dates Feb - June PACING

Zearn Digital Independent

Lessons NOTE – Zearn’s Grade 6 Missions are not in the same order as the Math

Modules.

Instructional Notes

Week 31 Wed ½ Day Thurs No School

4/26-4/30 M5: Lesson 13/14 and 17/18

Mission 1 Lessons 14 and 15 to replace Module Lessons 15-16

Combine Lessons 13/14, they have the same objective/cover the same concept, solving volume and real world applications. Use Lesson 13 problem set 1, 2, and 6 to supplement Lesson 14. Omit Lesson 15 and 16, these lessons require students to complete hands-on activities. Use Zearn as this objective/concept is covered in Mission 1 Lessons 14 and 15. Combine Lessons 17/18, same objective/concept of surface area of three dimensional figures. Include using the surface area formula in Lesson 17. Combine problem sets and exit tickets. If students need additional support, assign Zearn Mission 1, Lesson 12 to demonstrate surface area using unit cubes.

Week 32 Tues & Wed Testing

5/3-5/7 M5: Lesson 19 M6: Lesson 1

Mission 1 Lesson 16 to support Module Lesson 19 *Note- This lesson contains guided practice only, no independent practice Mission 8 Lesson 1 or 2 to support Lesson 1 *look at these lessons and choose the one that best meets your student’s needs

Omit 19A as this is an additional lesson.

Week 33 5/10-5/14 M6: Lesson 2, 3 Mission 8 Lessons 3, 4 or 5 to




Wed ½ Day Thurs No School

support Lesson 2 and 3 *look at these lessons and choose the one that best meets your student’s needs.

Week 34 5/17-5/21 M6: Lesson 4/5, 6 Mission 8 Lesson 6, 7, or 8 to support Lessons 4 and 5. *look at these lessons and choose the one that best meets your student’s needs. Mission 8 Lesson 9 to support Lesson 6

Combine Lessons 4 and 5, they have the same objective/cover the same concept, histograms. Combine problem sets and exit tickets.

Week 35 5/24-5/28 M6: Lesson 7, 8, 9 Mission 8 Lesson 10 to support Lessons 7 and 8 Mission 8 Lesson 11 to support Lesson 9

Week 36 Mon- No School

5/31-6/4 M6: Lesson 10/11, 12 Mission 8 Lesson 12 to support Lesson 10-11 Mission 8 Lesson 13 to support Lesson 12

Combine Lessons 10/11, they have the same objective/cover the same concept, describing distributions using the Mean and MAD. Combine problem sets and exit tickets

Week 37 6/7-6/11 M6: Lesson 13, 14/15/16

Mission 8 Lesson 15 to support Lesson 13

Combine Lessons 14/15/16, these lessons have the same objective, box plots. Combine the problem sets and exit tickets. Use 2 days to complete these lessons.

Week 38 6/14-6/18 M6: Lesson 17, 18 Mission 8 Lesson 16 and 17 to review/support Lessons 14, 15, and 16.

Week 39 6/21-6/24 M6: Lesson 19, 20, 21

grade 6 overview

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