2009 Mathematics Standards of Learning – Implementation Supported by Professional
Development
4th – 5th Grade Math PresentationSession #1
February 2011
2009 Mathematics Standards of Learning – Implementation Supported by Professional
Development
4th – 5th Grade Math PresentationSession #1
February 2011
1Parts taken from Michael Bolling’s (Mathematics Coordinator) – VSUP Presentation
December 9, 2010
The 2009 SOL and the new SOL Assessments
The 2009 SOL and the new SOL Assessments
2
• Increased rigor
• Higher-level questions
• Technology enhanced items
• Increased rigor
• Higher-level questions
• Technology enhanced items
y
The point U(-6, -3) is translated 3 units right. What are the coordinates of the resulting point, U′?
December 9, 2010
3
Gr 5 - New Content Changes
Equilateral
Scalene
Isosceles
Volume
5.4 – Create and solve single step and multistep practical
problems for addition, subtractions, multiplication and. INCLUDE DIVISION with and
without remainders.
5.8a – Find perimeter, areas and VOLUME in standard units
Measure and classify angles (added straight angles)
Classify triangles - add - Equilateral, Scalene, and Isosceles Triangle
COMPARE and ORDER fractions
and decimals
5.16 – Describe mean as Fair Share (M, M, & M as measures of
center
New Emphasized
Vocab.
Model one-step linear equations in one variable using
addition and subtraction.
What’s new/ in focus?Identify and
describe prime and composite
numbers
Identify and describe the
characteristics of even and odd
numbers
Division with decimals –
computation only
Estimate and measure length,
weight/mass, area, and liquid
volume
Measure and draw angles and triangles.
Line graphs
Stem and Leaf plots
5.5b – Create and solve single step and multistep practical
problems involving decimals.
5.7 – Evaluate whole number expressions using order of
operations limited to parentheses, +, -, X and /
5.19 – Investigate and recognize distributive property of addition
over multiplication
December 9, 2010 4
2.3 Identify/ write/compare halves, thirds, fourths, sixths, eighths, tenths
A sample of the progression of fractions.
K.5 Identify halves and
fourths
New content
1.3 Identify/ write halves, thirds, fourths
New content
5.2 a) Recognize equivalent
fractions/decimals.
B) compare and order fractions &
decimals
3.3 c) compare
fractions with like/unlike
denominators
4.2 a) compare and
order fractions /mixed
numbers6.2 a)
compare/order fractions, decimals,
and %
6.4 model multiplication and
division of fractions
7.1 c) Compare and order fractions,
decimals, percents, and scientific
notation
December 9, 2010
2.a,b - Identify parts of sets and/or regions that represent halves, thirds, fourths, sixths, eighths, and tenths. Write the
fractions ( and not just unit fractions)
Which model represents 2/3 of a set?
December 9, 2010
FAIR SHAREFAIR SHARE
2
2
2
2
2
Third grade adds 1/12ths(previously students will learn ½, ¼, 1/3, 1/8, 1/10)
Third grade adds 1/12ths(previously students will learn ½, ¼, 1/3, 1/8, 1/10) 2
2
2
December 9, 2010
FAIR SHAREFAIR SHARE
2
2
2
2
2
Third grade adds 1/12ths(previously students will learn ½, ¼, 1/3, 1/8, 1/10)
Third grade adds 1/12ths(previously students will learn ½, ¼, 1/3, 1/8, 1/10) 2
2
2
December 9, 2010
Grades 1 & 2 – Unit Fractions (1/2, 1/3, ¼, 1/6, 1/8, 1/10)
Grades 1 & 2 – Unit Fractions (1/2, 1/3, ¼, 1/6, 1/8, 1/10)
13
1
0
14
12
Help them understand the size relationship between ¼, 1/3, and ½ of a given whole.
Talk about:Which is greater? Which is less?
December 9, 2010
3.3c – Compare Fractions using >, <, or = signs)(1/2, 1/3, ¼, 1/8, 1/10, 1/12)
3.3c – Compare Fractions using >, <, or = signs)(1/2, 1/3, ¼, 1/8, 1/10, 1/12)
13
12
14
10
18
110
4.2 Compare and order fractions/mixed numbers (Number line will be important!)
112
December 9, 2010
4th Grade - Comparing fractions to benchmarks
Gr. 3 will add and subtract
fractions with denominators of 12
or less. They will also learn X
facts through 12’s (was 9’s)
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
11
3.7 The student will add and subtract proper fractions having denominators of 12 or less.
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
12
4.3 d) The student will, given a model, write the decimal and fraction equivalents.
0.2
or
4.2 equivalent fractions
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
13
4.13 b) The student will represent probability as a number between 0 and 1, inclusive.
Jennifer has 12 marbles.
1 Blue
3 Red
8 Green
Where on the number line would you place an arrow to show the probability of choosing a green marble?
8/12
2/3
December 9, 2010
The Number line!The Number line!
14
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December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
16
6.20 The student will graph inequalities on a number line.
4
4
x
x
4
4
Students will need a solid conceptual
understanding of inequalities before going
to Middle School based
upon the NUMBER
LINE!
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
17
8.5 b) The student will find the two consecutive whole numbers between which a square root lies.
Between which two square roots does 5 lie?
Between which two whole numbers does lie?Between 5 and 6 Between
SQR(16) and SQR (36)
SQR (16) (25) (36) (49)
4 5 6 7
SQR (16) (25) (36) (49)
4 5 6 7
How you can help.Necessary Background:
Students will need a thorough understanding and mastery of the number line and perfect squares.
(also numbers, fractions, and decimals)
December 9, 2010 18
3.20 a)
identity/
commutative
properties
for add/mult
Equality and Properties – preparation for justifications
1.18 demonstrate
equality using equal
signs
New from grade 3
2.22 demonstrate
an understanding
of equality using = and ≠
New content
4.16 b) associative property for
add/mult
Newfrom grade 7
5.19 distributive property of
multiplication over addition
New from grade 76.19 a-c) investigate and identify property of +/X, multiplicative
property of zero, inverse property for
multiplication
7.16 a-e) apply properties with real
numbers, comm/associative property of +/X,
distributive, +/X identity,
+/X inverse, X property of 0Leading into students giving justifications to steps when
solving equations and inequalities in MS and HSLeading into students giving justifications to steps when
solving equations and inequalities in MS and HS
December 9, 2010
Equations and InequalitiesEquations and Inequalities
What does the equal sign mean?
What does the equal sign mean?
December 9, 2010
EqualityEquality
Connected to N&NS SOL 2.1c
1.18 The student will demonstrate an understanding of equality through the use of the equal sign.
2.22 The student will demonstrate an understanding of equality by recognizing that the symbol = in an equation indicates equivalent quantities and the symbol ≠ indicates that quantities are not equivalent.
Connected to N&NS SOL 2.1c
1.18 The student will demonstrate an understanding of equality through the use of the equal sign.
2.22 The student will demonstrate an understanding of equality by recognizing that the symbol = in an equation indicates equivalent quantities and the symbol ≠ indicates that quantities are not equivalent.
5 + 3 =AND THE ANSWER IS…….?
Now students should think about options to balance the equation on the right side. List 5 options that would make the sentence balance?
8, 10-2, 1+7,
5 + 3 2+5+1, 3+10-5
5 + 3 =AND THE ANSWER IS…….?
Now students should think about options to balance the equation on the right side. List 5 options that would make the sentence balance?
8, 10-2, 1+7,
5 + 3 2+5+1, 3+10-5
20
Where are we headed?
December 9, 2010
Equalities -2009 SOL 4.16a recognize/demonstrate meaning (thinking) of equality in an equation.
Equalities -2009 SOL 4.16a recognize/demonstrate meaning (thinking) of equality in an equation.
8 = 1 + 7
3 + 5 = 5 + 32 + 3 = 2 x 3
True or False?
7 x 4 = 4 + 4 + 4 + 4
What will the students say?
21
How many different ways can you show
9 = 9?
December 9, 2010
SOL 1.18 demonstrate equality using an equal signSOL 1.18 demonstrate equality using an equal sign
http://illuminations.nctm.org/ActivityDetail.aspx?id=33
SOL 2.22 demonstrate understanding of equality and not equal signsSOL 2.22 demonstrate understanding of equality and not equal signs
Equal Sign=
Not Equal Sign=
December 9, 2010 23
Inequalities 2009 SOL 3.20 (C.F. - Essential Understanding )
Inequalities 2009 SOL 3.20 (C.F. - Essential Understanding )
2 34 4
December 9, 2010 24
3 34 4
Equalities 2009 SOL 3.20 (C.F. - Essential Understanding )
Equalities 2009 SOL 3.20 (C.F. - Essential Understanding )
Grade 1
The order with which you add the numbers
doesn’t change
anything. Both sides are
still equal.
Commutative
Property of
addition
December 9, 2010 25
December 9, 2010 26
3 34 4
Equalities - 2009Equalities - 2009
Gr 5 – Distributive Property of Multiplication over Addition
2 X ( 3 + 1 ) ( 2 X 3 ) + (2 X 1)
December 9, 2010 27
Equalities (use to prove properties)
Equalities (use to prove properties)
http://illuminations.nctm.org/ActivityDetail.aspx?id=26
December 9, 2010
Equalities/Properties2009 SOL
Equalities/Properties2009 SOL
28
Identity Property of Addition/Multiplication
8 + 0 = 8
8 x 1 = 8
Commutative Property of Addition/Multiplication
4 + 3 = 3 + 4
2 x 5 = 5 x 2
Gr. 4 – Associative property of addition and multiplication
Gr. 5 Distributive Property of
multiplication over addition
December 9, 2010 29
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
Using a cup and candy corn, construct a model for
J = 6
December 9, 2010 30
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
How many
pieces are
represented by
the jack-o-
lantern?
December 9, 2010 31
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
Using your cups and candy corn, construct a model for
J + 4 = 7
December 9, 2010 32
Modeling One-step Linear Equations2009 SOL 5.18c
Modeling One-step Linear Equations2009 SOL 5.18c
J = 3
pieces of candy
December 9, 2010 33
What equation is modeled below?What equation is modeled below?
B + 2 = 9
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
5.8 c) The student will model one-step linear equations in one variable, using addition and subtraction.
3 5x = x
= 1
December 9, 2010
We can all continue concept of variable (Previous Grades)
We can all continue concept of variable (Previous Grades)
?
December 9, 2010 36
5.7 Order of
Operations
6.8 Order of
Operations
no { }, | |
Only ( )
7.13 evaluate algebraic
expressions
7.3 operations
with integers
8.1 simplify numerical expressions involving positive exponents,
using rational numbers, order of operations, and
properties to justify
Alg1.1 represent verbal quantitative situations algebraically/evaluate expressions for given replacement values of
variables
New from grade 7
New from grade 7
Expressions and Operations
New content including
(modeling)
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
37
Order of Operations
40 16 2 (1 3)
340 2 2 (1 3)
3 3x x evaluate , given x = -2
5.7
6.8
7.13b
1st2nd
3rd
December 9, 2010 38
5.16 Mean as
Fair Share
6.15 Mean as Balance
Point
New content New content
Statistics
Alg1.9 Standard Deviation
Alg1.9 – Standard deviation, mean absolute deviation, variance, dispersion, z-scores
New content
Alg2.11 Normal
Distributions
New content
December 9, 2010
Mean as Fair ShareMean as Fair Share
108
3
Average: (10 + 8 + 3) / 3 items = 7
December 9, 2010
Mean as Fair ShareMean as Fair Share
7 7 7
Average: (10 + 8 + 3) / 3 items = 7
December 9, 2010
Mean as Balance PointMean as Balance Point
41
7
3 8 10
It’s all about the total distance away from the
“mean/average”
Helps to create a foundation to understand
“absolute value”
December 9, 2010
SOL 4.14 – Collect, organize, display, interpret data from a variety of graphs
SOL 4.14 – Collect, organize, display, interpret data from a variety of graphs
• collect and organize data• Recollect and compare data• observe, measure, surveys,
experiments• Construct line plots, bar graphs and
picture graphs to represent the data• Read and Interpret the data in these
graphs
• collect and organize data• Recollect and compare data• observe, measure, surveys,
experiments• Construct line plots, bar graphs and
picture graphs to represent the data• Read and Interpret the data in these
graphs
December 9, 2010
Statistics in Algebra One
Statistics in Algebra One
Collect data, display and analyze data, understand the behavior of data sets, understand how data is spread about the mean, how is this used to inform decisions
Collect data, display and analyze data, understand the behavior of data sets, understand how data is spread about the mean, how is this used to inform decisions
43http://www.mathwire.com/
How can you help?
Help students
become
comfortable in
collecting,
displaying, and
analyzing data.
They should also
be able to make
logical predictions
from the data.
December 9, 2010
Ages of parents and grandparents
Talk about :
• how data is sometimes grouped in clusters
• how sometimes there are data points that lie far from the group of data.
Discuss what conclusions can be made?
M T W T F Sat Sun
Number of students ordering lunch
Ask extended questions:
• Define the days where the number of students ordering lunch is increasing.
• Which days is the number of students ordering lunch decreasing?
• Where is the data not increasing?• Where is the data not decreasing?
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
45
3.6 The student will represent multiplication and division, using area, set, and number line models…
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
46
3.9d The student will estimate…area and perimeter.
The curriculum framework says the student will also measure to
determine area and perimeter.
December 9, 2010
Higher Order Thinking Skills Higher Order Thinking Skills Connected to N&NS SOL 3.2
1.6 The student will create and solve
one-step story and picture problems using basic addition facts with sums 10 18 or less and the corresponding subtraction facts.
2.8 The student will create and solve
one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs
3.4 The student will estimate solutions
to and solve single-step and multistep problems involving the sum and difference of two whole numbers, each 9,999 or less, with or without regrouping.
Connected to N&NS SOL 3.2
1.6 The student will create and solve
one-step story and picture problems using basic addition facts with sums 10 18 or less and the corresponding subtraction facts.
2.8 The student will create and solve
one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs
3.4 The student will estimate solutions
to and solve single-step and multistep problems involving the sum and difference of two whole numbers, each 9,999 or less, with or without regrouping.
47
the use of two or moreoperations; and operations can be different.
December 9, 2010
Emily is reading the latest Magic
Maggie book. She reads 12
pages each day. After 7 days,
Emily still has 20 pages left to
read. How many pages are in
Emily's book?
Emily is reading the latest Magic
Maggie book. She reads 12
pages each day. After 7 days,
Emily still has 20 pages left to
read. How many pages are in
Emily's book?
48
Grade 3Zach had 64 ounces of soda.
He poured 8 ounces into each of 5 glasses. How much soda was
left over?
K – 1 - Modeling to solve word problems
Tamara had 3 pennies.
She got 5 pennies for cleaning her room.
Then she lost 2 pennies.
How many pennies does she now have?
4.4b & 4.5d – Solve single and multi-step practical problems involving add/sub/multi. of whole number and add/sub of fractions, and decimals
December 9, 2010
Students need opportunities to solve various problem types through modeling, reasoning, and reflection to strengthen their mathematics understandings and use of concepts and skills.
Students need opportunities to solve various problem types through modeling, reasoning, and reflection to strengthen their mathematics understandings and use of concepts and skills. Let the students struggle, take a risk at getting it
wrong, explain why, re-think, re-do!
Check out this site:
http://www.mathwire.com/problemsolving/probsk12.html#k12number
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.
5.5 The student will
a) find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and
b) create and solve single-step and multistep practical problems involving decimals.
5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.
5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.
5.5 The student will
a) find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and
b) create and solve single-step and multistep practical problems involving decimals.
5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.
50
5.5 b) Michael jogged 3.4 miles each day for 3 days. Jennifer jogged 4.2 miles each day for the same 3 days. What is the difference between the number of miles Jennifer jogged and the number of miles Michael jogged on these 3 days?
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
51
7.5 c) The student will describe how changing one measured attribute of a rectangular prism affects its volume and surface area.
Describe how the volume of the rectangular prism shown (height = 8 in.) would be affected if the height was
increased by a scale factor of ½ or 2. V = h X 3 X 5
8 in.
5 in.
3 in.
The volume would be cut in half or doubled accordingly.
V = (8)(15) - originalV = (4)(15) – height is halfV = (16)(15) – height is double
SA = 2(l*w)+ 2(w*h) + 2(l*h)
How you can help.
Necessary Background:
Give the students word problems to
solve. Then ask them what would
happen if one variable changed.
Example: If you ran 3 minutes each day at recess
for a total of 5 days. How many minutes would you
have run for the week?
Next: Ask how many total minutes would you have
run, if on Tuesday only, you ran more than usual
and ran 8 minutes instead.
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
52
8.11The student will solve practical area and perimeter problems involving composite plane figures.
Find the area of
the shaded region. A1
A2
Blue Area = A1+A2
A2 = Area of Square
Blue Area = A1 - A2
A1 = Area of Circle
December 9, 2010
Assessing Higher-level Thinking Skills
Assessing Higher-level Thinking Skills
53
A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.
Which class had the most students scoring higher than 83?
Class A has 36 students and Class B has 20 students. Which class has more students scoring above 83?
25% of 36 = 9
50% of 20 = 10
Longer (to 98)?
December 9, 2010
Note: Blueprints Changes
Note: Blueprints Changes
- 54 -
• Some Reporting Categories Combined
• Watch the growing emphasis on the Statistics, Patterns, Functions, and Algebra Reporting Category shown on the next slides
December 9, 2010
December 9, 2010 56
December 9, 2010 57
December 9, 2010
A focus on content plus….
a balance between conceptual and procedural approaches.
include relevant and real world applications.
give students intentional vertical connections to other grade level content and practices.
reflection time – to answer “the why”, “what if”!
A focus on content plus….
a balance between conceptual and procedural approaches.
include relevant and real world applications.
give students intentional vertical connections to other grade level content and practices.
reflection time – to answer “the why”, “what if”!
58
We Must Provide….We Must Provide….
December 9, 2010 - 59 -
Technology Enhanced Items (TEI) Technology Enhanced Items (TEI)
Format of Questions:
• Fill in the blank• Click and drag• Hot-spots: Select one or more answer options, placing points on
coordinate planes• Creation of graphs
• Approximately ten practice questions for each mathematics test, Grades 3-8 and EOC addressing – February 2011
• increased rigor for existing SOL• items that address new SOL• technology enhanced items
Format of Questions:
• Fill in the blank• Click and drag• Hot-spots: Select one or more answer options, placing points on
coordinate planes• Creation of graphs
• Approximately ten practice questions for each mathematics test, Grades 3-8 and EOC addressing – February 2011
• increased rigor for existing SOL• items that address new SOL• technology enhanced items
December 9, 2010 - 60 -
Mathematics Standards of Learning Implementation Timeline
Mathematics Standards of Learning Implementation Timeline
2010 – 2011 • Teach old and new SOL content• Field Test items on new 2009 SOL – live test items on 2001 standards• Grade 3 live test is still cumulative but field test items on
new content is only from grade 3 content
2011-2012• New 2009 SOL taught and fully assessed• New Grade 3 assessment covers 2009 grade 3 content only•
2012-2013• Gr. 3-5 technology enhanced items are live spring 2013
December 9, 2010 61
As the Virginia Department of Education revised the Standard of Learning assessments to
increase the level of rigor and include higher-level questions (M. Bolling, VDOE, 2010)
teachers will need to prepare students to respond well to these kinds of questions.
December 9, 2010 62
1. Can be solved or explained in a variety of ways
2. Focus on conceptual aspects of mathematics
3. Have the potential to expose student understanding and misconceptions
5. Lend themselves to a scoring rubric (see the rubric included)
PIVOTAL QUESTIONSThey serve a vital and critical role inunveiling student understanding and
misconceptions in ways that knowledge-recall questions do not allow.
December 9, 2010 63
Try to make some simple shifts in what you
expect from students.
That means….asking it differently!
Here are some examples of how you might
adjust a few typical elementary concepts.
December 9, 2010 64
• How did you arrive at that answer?• Why do you think that?• What have you discovered?• Have you thought of another way this could be done?• Does that make sense?• Does that always work?• How could we prove that?• Have we solved a problem similar to this one?• Is that the only possible answer?• Is your solution reasonable?• Is there a real-life situation where this could be used?• Where else would this strategy be useful?• Do you see a pattern? Is there a general rule?• What other questions does this bring up?• What is the math in this problem?• Have you tried making a guess?• Would another recording method works as well or better?• Give me another related problem.• Is there another way to draw or explain that?• How did you organize your information?• Would it help to draw a picture?
Incorporate Good Mathematical Questioning
December 9, 2010 65
Try to make some simple shifts in what you expect from students.
That means….asking it differently!
• Find a rectangle in the classroom.
• What shape are the student desks?
Instead ask:How do you know the chalk board is a rectangle?How do you know the student desks are not a square?
December 9, 2010 66
Try to make some simple shifts in what you expect from students.
That means….asking it differently!
What is the probability of drawing a red marble from bag one?
Instead ask:If you close your eyes, reach into a bag, and remove 1 marble, which bag would give you a better chance of picking a blue marble?
How could we prove that?
Is there a real-life situation where this could be used?
75 red25 blue
40 red20 blue
100 red25 blue
1
2
3
December 9, 2010 67
Before…….
Write 0.1 as a fraction.Or Reduce 2/20.
After…..
Write 0.1 with three different equivalent numbers.
Or
Which of the following are equivalent to 0.1?{ 1/10, 10%, .02, 2/20, 1%, 0.10}___________________________________________
December 9, 2010 68
Try asking:
Write two numbers that are greater than 95.867 by re-arranging only two digits for each new number created. Defend your answer choice.
Instead of:
Fill in the blank with > or <:
95.867 ____ 95.876
December 9, 2010 69
Before:
Identify each angle as a right angle, acute angle, or an obtuse angle?
After:
Draw a playground using at least five different angles that are between 45 degrees and 125 degrees. Name each resulting angle.
December 9, 2010 70
Before:
The temperature of the water in a swimming pool is 51°F. Since the freezing point of water is 32°F, how many degrees would the temperature of thewater have to drop to reach the freezing point?
After:
If the water in a swimming pool was 67 degrees at 8:00 am, and at 11:00 am that morning it had risen 8 more degrees, how many more degrees would the water need to rise in order to swim in water that was 80 degrees?
December 9, 2010 71
72
Content moved away from Gr. 4
Remove
id ordered pairs in the
first quadrant of coordinate
plane
Have students apply only
Vocabulary – flip, slide, turn
from grade 3 – compare fractions, id congruent and non-congruent shapes,
perimeter and area, analyze properties of 2-D and 3-D figures,
From grade 2 - Certain-likely-unlikely-
impossible
Describe the path of shortest distance
between two points on a flat
surface.
Moving to 6th grade
Estimate conversions between metric and US Customary Units (weight, length,
volume) – still have to do it among metric units and among US customary units.
December 9, 2010
73
Gr 4 - New Content Changes
Associative Property
Equivalent
Tons
Miles
4.2c – Id the division statement that represents a fraction
4.3d Given a model, write the decimal and fraction equivalents
4.2a – compare and order
fractions and mixed numbers
with like and unlike
denominators.
Use denominators of
12 or less by comparing to benchmarks (number line)
Equivalent fractions through
twelfths using regions, set models, and
measurement models (#line)
4.4d & 4.4d Solve single step and multi-step +, -, X, problems with whole numbers, fractions, and
decimals
4.9 – determine elapsed time in hours and minutes within a 12 hour
period
4.12a, b – define polygon. Identify polygons with 10 or fewer sides
4.13b – Represent probability as a
number between 0 and 1 inclusive
( need fractions on a number line)
New Emphasized
Vocab.
4.16 a/b (from 7.3a) recognize
and demonstrate the meaning of equality in an
equation. Investigate the
equality in + and X equations that
demonstrates the associative
property of + and X.
What’s new/ in focus?
December 9, 2010
ResourcesResources
74
• Blueprints are currently available – effective in 2011-2012 http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/review.shtml
• Formula sheets for 6-8 and EOC are currently available – effective 2011-2012
http://www.doe.virginia.gov/testing/test_administration/ancilliary_materials/2011-12/index.shtml
• Curriculum Framework – http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/review.shtml
• New Enhanced Scope and Sequence – coming soon : summer 2011
Will include differentiation strategies for all learners.
• Math Resource page http://www.doe.virginia.gov/instruction/mathematics/high/index.shtml
• Vocabulary http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/vocabulary/index.shtml
• Vertical Articulation Documents – handouts
• Blueprints are currently available – effective in 2011-2012 http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/review.shtml
• Formula sheets for 6-8 and EOC are currently available – effective 2011-2012
http://www.doe.virginia.gov/testing/test_administration/ancilliary_materials/2011-12/index.shtml
• Curriculum Framework – http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/review.shtml
• New Enhanced Scope and Sequence – coming soon : summer 2011
Will include differentiation strategies for all learners.
• Math Resource page http://www.doe.virginia.gov/instruction/mathematics/high/index.shtml
• Vocabulary http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/vocabulary/index.shtml
• Vertical Articulation Documents – handouts
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