Module 102 Rigor and Balance AC 1 wwwachievethecoreorg Essential Questions How does the Instructional Materials Evaluation Tool IMET reflect the major features of the Standards and the Shifts ID: 784123
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Slide1
Reviewing Using the Instructional Materials Evaluation Tool: Mathematics
Module 102: Rigor and Balance (AC 1)
www.achievethecore.org
Slide2Essential Questions
How does the Instructional Materials Evaluation Tool (IMET) reflect the major features of the Standards and the Shifts?
What understandings support high-quality, accurate application of the IMET metrics?
Slide3GoalsUnderstand how aligned materials embody the shifts inherent in the Common Core State
StandardsUnderstand the precise meaning of each metric of the IMET
Recognize examples and non-examples related to each
metric
of
Alignment Criterion 1
Slide4Non Negotiable vs. Alignment Criteria
Non- Negotiable CriteriaAlignment Criteria
Each metric rated Meets/Does Not Meet
Each metric rated Meets/Partially Meets/Does Not Meet
Every metric must be met to rate the criterion as Meets
Must receive 5 out of 6 points to rate the criterion as Meets
Slide5Alignment Criterion 1: Rigor and Balance
Slide6Alignment Criterion
1: Materials must reflect the balances in the Standards and help students meet the S
tandards
’ rigorous expectations.
Rigor
IMET p. 17
Slide7What Is
Rigor?
Slide8The Three-Legged
Stool
AC 1 Metric 1A: The materials support the development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content Standards or cluster headings.
Conceptual Understanding
IMET pp. 18-19
Slide10Conceptual Understanding
Teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives
Students are able to see math as more than a set of mnemonics or discrete
procedures
Conceptual understanding is about mathematical ideas, often distinct from context.
Conceptual understanding supports the other aspects of rigor (procedural skill and
fluency,
and application)
Slide11IMET p. 19
Slide12AC 1A: Is conceptual understanding attended to thoroughly where the Standards set explicit expectations for understanding or
interpreting?
4.OA.A
Use the four operations with whole numbers to solve problems.
4.OA.A.1
Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
4.OA.B.4
Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or
composite.
4.MD.A.3
Apply the area and perimeter formulas for rectangles in real world
and mathematical
problems.
For example, find the width of a
rectangular room
given the area of the flooring and the length, by viewing the
area formula
as a multiplication equation with an unknown factor
.
Handout p. 2
IMET p. 18
Slide13AC 1A: Do the materials feature high-quality conceptual problems
and conceptual discussion questions?
[I]n solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Problems are problems because students haven’t yet learned how to solve them; students are learning from solving
them.
- K-8 Publishers’ Criteria, Spring 2013, p.
1
7
IMET p. 1
8
Slide14AC 1A: Do the materials feature high-quality conceptual problems and conceptual discussion questions?
4.NF.A
Handout p. 3
IMET p. 18
Slide15AC 1A: Do the materials feature high-quality conceptual problems
and
conceptual discussion questions
?
Which
number is larger?
1.7 or 17
twelfths
Explain how you can tell without drawing
a
picture
.
4.NF.C
Handout p. 3
IMET p. 18
Slide16AC 1A: Do the materials feature opportunities to identify correspondences across mathematical representations?
Handout p. 4
IMET p. 18
Slide17AC Metric 1A: Review a Full Lesson
Review the grade 4 lesson on pp. 5-8 of
your handout.
Note evidence for each question associated with AC Metric
1A on p. 19 of your IMET.
Discuss:
Gut check: Would these materials meet, partially
meet,
or not meet AC
1A?
What is your evidence?
What other
things
would you want to look at in these materials to determine your rating?
Slide18AC Metric 1B:
The materials are designed so that students attain the fluencies and procedural skills required by the Standards.
Procedural Skill and Fluency
IMET pp. 20-21
Slide19Procedural Skill and Fluency
The Standards require speed and accuracy in calculation.
Material
s
structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts
Slide20Required Fluencies in K-6
Grade
Standard
Required Fluency
K
K.OA.5
Add/subtract within 5
1
1.OA.6
Add/subtract within 10
2
2.OA.2
2.NBT.5
Add/subtract within 20 (know single-digit sums from memory)
Add/subtract within 100
3
3.OA.7
3.NBT.2
Multiply/divide within 100 (know single-digit products from memory)
Add/subtract within 1000
4
4.NBT.4
Add/subtract within 1,000,000
5
5.NBT.5
Multi-digit multiplication
6
6.NS.2,3
Multi-digit division
Multi-digit decimal operations
Slide21IMET p. 21
Slide22AC 1B: Is progress toward fluency and procedural skill interwoven with students’ developing conceptual understanding
of the operations in question?
Handout p. 9
IMET p. 20
Slide23AC 1B: Do the materials in grades K–6 provide repeated practice
toward attainment of fluency Standards?
IMET p. 20
Slide24AC Metric 1B: Review a Full L
esson
Review the grade 4
lesson on pp. 10-13 of your handout.
Note evidence for each question associated with AC Metric
1B on p. 21 of your IMET.
Discuss:
Gut check: Would these materials meet, partially
meet,
or not meet AC
1B?
What is your
evidence?
What
other
things
would you want to look at in these materials to determine your rating?
Slide25AC Metric 1C:
The materials are designed so that teachers and students spend sufficient time working with applications, without losing focus on the Major Work of each grade.
Application
IMET pp. 22-23
Slide26Application
Students can use appropriate concepts and procedures for application even when not prompted to do so.
Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in
K-2, 3-5,
and 6-8
Slide27IMET p. 23
Slide28AC 1C: Are there single-
and multi-step contextual problems that develop the mathematics of the grade, afford opportunities for practice, and engage students in problem solving?
A grower packs 4,568 peaches. He packs the most peaches possible, dividing them equally into 9 boxes, and then gives away the remaining peaches.
How many of the remaining peaches does he give away?
If he sells 7 boxes, how many peaches does he have left?
Handout p. 14
IMET p. 22
Slide29AC 1C: Do application problems particularly stress applying the Major Work of the grade?
1
)
A clown
needs 275 balloons
for a party he
is
going to, but the balloons only
come
in packs of
8.
How many packs of balloons
does
he need to buy?
2
) A florist splits 878 flowers into vases by putting 9 flowers in each vase. She needs more flowers to fill the last vase. How many more flowers does she need so that the last vase also has 9?
Handout p. 15
IMET p. 22
Slide30AC 1C: Does modeling build slowly across K–8, with applications that are relatively simple in earlier grades and when students are encountering new content? In grades 6–8, do the problems begin to provide opportunities for students to make their own assumptions or simplifications in order to model a situation mathematically?
2.OA.A.1
A
pencil costs 59 cents, and a sticker costs 20 cents less. How much do a pencil and a sticker cost together
?
7.EE.B.4
Shelbi is running in a
half marathon
today. About ½ hour before the race, she parks her car in a garage about ¼ mile from the starting line. The prices for parking are shown in the following table:
As
she is running, she remembers that she only has $13. What is the slowest pace Shelbi can run, in minutes per mile, and still pay less than $13 for parking? Explain your answer. State any assumptions you made.
Handout p.
16
IMET p. 22
Less than 1 hour
$8
1 hour to less than 2 hours
$12
2 hours to less than 3 hours
$15
3 hours or more
$18
Slide31AC Metric 1C: Review a Full Lesson
Review the grade 4 lesson on pp. 17-20 of your handout.
Note evidence for each
question associated with AC Metric 1C
on p. 23 of your IMET.
Discuss:
Gut
check:
Would these materials meet, partially meet, or not meet AC 1C?
What is your
evidence?
What
other
things
would you want to look at in these materials to determine your
rating?
Slide32IMET p. 24
Slide33Wrapping Up
Slide34Alignment Criterion 1 and Metrics
AC #1: Balance and Rigor1A: Conceptual Understanding1B: Procedural Skill and Fluency
1C: Application
Slide35Essential Questions -- Discuss
How does the Instructional Materials Evaluation Tool (IMET) reflect the major features of the Standards and the Shifts?
What understandings support high-quality, accurate application of the IMET metrics?