# Grade 6: Alignment to Mathematics

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Grade 6:

Alignment to Mathematics Grade-Level Standards

Slide2

Session Objective

The purpose of these materials is to help develop understanding of the expectations of high-quality summative assessment items. The concepts shown throughout these modules can be useful for classroom questioning and assessment, but the items themselves may need to be slightly modified.

Slide3CCSSO Section C: Align to Standards – Mathematics

Criterion C.1:

Focusing strongly on the content most

needed for success in later

mathematics

Criterion C.2:

Assessing a balance of concepts, procedures, and applications

Criterion C.3:

Connecting practice to content

Criterion C.4:

Requiring a range of cognitive demand

Criterion C.5:

Ensuring high-quality items and a

variety of item types

Slide4Slide5

Ten Principles of CCSS-Aligned Items

1. Most items aligned to standards in supporting clusters connect to the major work of the grade.

2.

Items are designed to address the aspect(s) of rigo

r (conceptual understanding

, procedural skill, and application) evident in the language of the content standards.

3. Items are designed to attend to content limits articulated in the standards.

4. Most items aligned to a single content standard should assess the central concern of the standard.

5. Representations are well suited to the mathematics that students are learning and serve

an important purpose within the item itself.

6.

Items use mathematically precise language, are

free from mathematical errors or ambiguities,

and are aligned to the mathematically appropriate standard.

7. The demands of items measuring the Standards for Mathematical Practice are appropriate to the targeted grade level.

8.

Item types are chosen to match the item’s purpose and as part of the evidence required by the standards.

9.

Most items measuring the Standards for Mathematical Practice are also aligned to content standards representing the major work of the grade.

10. Items written at the cluster or domain level measure key integration points not necessarily articulated in individual standards but plausibly implied directly by what is written.

Slide6Alignment Principle #1

Most items aligned to standards in supporting

clusters

connect to the major work

of the grade.

Slide7Most items aligned to standards in supporting clusters connect to the major work of the grade.

6.G.A.2. 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. [

standard intentionally shortened to fit slide

]

Slide8Alignment Principle

#2

Items are designed to address the

aspect(s

) of

rigor

(conceptual understanding, procedural skill, and application) evident in the language of the content standards.

Slide9Items are designed to address the component(s) of rigor (

conceptual understanding, procedural skill, and application) evident in the language of the content standards.

6.NS.C.6b

.

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.

Slide10Items are designed to address the

aspect(s) of rigor (conceptual understanding, procedural skill, and application) evident in the language of the content standards.

6.RP.A.3c.

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.

Enter the unknown value that makes this statement true:

45 is ____% of 50.

Slide11Items are designed to address the

aspect(s) of rigor (conceptual understanding, procedural skill, and application) evident in the language of the content standards.

6.RP.A.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.

Alan is making banana

bread. The ratio of the number of cups

of

mashed

bananas

to the number of cups of flour for his recipe is 6:3

.

Alan uses 3 cups of mashed bananas to make 1 loaf. How many cups of flour will he use?

Erik

uses Alan’s recipe to make banana bread. Erik uses 9 cups of flour in total. How many loaves does Erik make?

Slide12

Alignment Principle

#3

Items are designed to attend to

content limits

articulated in the standards.

Slide13Items are designed to attend to content limits articulated in the standards.

6.EE.B.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

.

Slide14Alignment Principle

#4Most items aligned to a single content standard should assess the

central concern

of the standard.

Slide15Most items aligned to a single content standard should assess the central concern of the standard.

Central Concern

Not the Central Concern

6.NS.B.2

. Fluently divide multi-digit numbers using the standard algorithm.

Slide16Alignment Principle

#5

Representations

are well suited to the mathematics that students are learning and serve an important purpose within the item itself.

Slide17

Representations are well suited to the mathematics that students are learning and serve an important purpose within the item itself.

6.RP.A.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.

The diagram shows the unit rate for making copies on a copy machine.

Which table shows data for the same copy machine?

Slide18Alignment Principle

#6

Items use mathematically precise language, are

free from mathematical errors or ambiguities

, and are aligned to the mathematically appropriate standard.

Slide19Items use mathematically precise language, are

free from mathematical errors or ambiguities, and are aligned to the mathematically appropriate standard. Wyatt hiked 6 miles in 2 hours. How many miles can he hike in 9 hours?

✗

✔

6.RP.A.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.

Wyatt hiked 6 miles in 2 hours. At this same rate, what is the total number of miles he would hike in 9 hours?

Slide20Alignment Principle

#7

The demands of items measuring the Standards for Mathematical Practice are

appropriate

to the targeted grade level.

Slide216.G.A

Solve real-world and mathematical problems involving area, surface area, and volume.MP1. Make sense of problems and persevere in solving them.

The demands of items measuring the Standards for Mathematical Practice are appropriate to the targeted grade level.

Slide22Alignment Principle

#8

Item types

are chosen to

match

the item’s

purpose

and as part of the

evidence

required by the standards.

Slide23Item types are chosen to match the item’s purpose and as part of the evidence required by the standards.

6.EE.5. 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.

Slide24Item types are chosen to match the item’s purpose and as part of the evidence required by the standards.

6.NS.C.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.

Slide256.RP.A.3.d

. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Slide26Alignment Principle

#9

Most items measuring the

Standards for Mathematical Practice

are also aligned to content standards representing the

major work

of the grade.

Slide27Most items measuring the Standards for Mathematical Practice are also aligned to content standards representing the major work of the grade.

MP4. Model with

mathematics.

6.EE.B.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.

Slide28Alignment Principle

#10

Items written at the

cluster or domain level measure

key integration points

not necessarily articulated in individual standards but plausibly implied directly by what is written.

Slide29Items written at the cluster or domain level measure key integration points not necessarily articulated in individual standards but plausibly implied directly by what is written.

6.NS.C. Apply and extend previous understandings of numbers to the system of rational numbers.

Slide30Ten Principles of CCSS-Aligned Items

1. Most items aligned to standards in supporting clusters connect to the major work of the grade.

2.

Items are designed to address

the aspect(s

) of rigo

r (conceptual understanding

, procedural skill, and application) evident in the language of the content standards.

3. Items are designed to attend to content limits articulated in the standards.

4. Most items aligned to a single

content standard

should assess the central concern of the standard.

5. Representations are well suited to the mathematics that students are learning and serve

an important purpose within the item itself.

6.

Items use mathematically precise language, are

free from mathematical errors or ambiguities,

and are aligned to the mathematically appropriate standard.

7. The demands of items measuring the Standards for Mathematical Practice are appropriate to the targeted grade level.

8.

9.

Most items measuring the Standards for Mathematical Practice are also aligned to content standards representing the major work of the grade.

10. Items written at the cluster or domain level measure key integration points not necessarily articulated in individual standards but plausibly implied directly by what is written.

Slide31Thank You!

## Grade 6: Alignment to Mathematics

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