| OUTCOME/
ESSENTIAL
QUESTION |
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| Why
is it important to know how to gather and organize
data to analyze? |
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*Name
values of variables (D.B2.K1)
*Describe a classroom of students using
variables (D.B2.K2)
*Gather, organize, and analyze data by using
variables, making data tables, and drawing bar
graphs (D.B2.A1)
*Distinguish between categorical and numerical
variables (D.B2.K1)
*Investigate the concept of averages (D.B2.K3)
*Find the median of a data sheet (D.B2.K3)
*Recognize the utility of the TIMS Laboratory Method
in problem-solving
*Solve a problem by using a graph and by extending
patterns in a data table (D.B2.A1)
*Recognize the importance of solving problems in
more than one way (N.B4.A1)
*Investigate the relationship between arm span and
height
*Represent data in a point graph (D.B2.K1)
*Use patterns in tables and graphs to make
predictions (D.B2.A1)
*Estimate quantities (N.B3.A2)
*Use a calculator when appropriate (N.B4.K1)
*Solve word problems (N.B4.A1)
*Communicate solutions orally and in writing
(D.B1.A3) |
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*Daily
assignments
*Unit Reviews
*Unit Assessments
*Teacher created materials
*DOM
*NWEAs
*Use of manipulatives
*Teacher observations
*Boardwork
*Games/Activities
*Group Activities
*KS Math Assessment |
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| Why is it important to know the relationship between length and
perimeter? |
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Geometric
Investigations
Numbers and Number Operations
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*Find the perimeters of irregular polygons (G.B2.K5)
*Find the area of irregular polygons (G.B2.K5)
*Use measurement to solve problems (G.B2.A1)
*Communicate problem-solving solutions
*Investigate the relationship between length and
perimeter (G.B2.A2)
*Gather, organize, and analyze data by using
pictures, variables, data tables, and point graphs
(D.B2.K1)
*Use patterns in tables and graphs to make
generalizations about data (A.B3.A1)
*Problem solve with area and perimeter (G.B2.A2)
*Justify a statement using mathematics (N.B1.A2)
*Identify goals
*Reflect on their own work
*Understand the purpose of a portfolio
*Identify angles in shapes (G.B1.K1)
*Identify angles as acute, right, or obtuse
(G.B1.K1)
*Estimate degree measures of angles (G.B2.A2)
*Find degree measures of angles (G.B2.K5)
*Build shapes and angles (G.B2.A1)
*Communicate solutions
*Link multiplication to counting things that come in
groups of equal size (N.B1.K1)
*Link multiplication to repeated addition (N.B4.K6)
*Use strategies to solve multiplication facts for 5s
and 10s (N.B4.K1)
*Write multiplication number sentences (N.B4.K5) |
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Objective/Skill continued-
*Calculate the value of collections of nickels and
dimes (N.B4.K1)
*Understand that other number systems exist
*Recognize key elements of Hindu-Arabic system
*Recognize and using patterns to write numbers
(A.B1.K2)
*Understand the ones' place and tens' place
(N.B2.K3)
*Understand the idea of counting by groups (N.B1.K1)
*Understand different representations of the same
amount (N.B1.A1)
*Understand the hundreds' and thousands' place
(N.B2.K3)
*Understand grouping and regrouping in base-ten
(A.B4.K1)
*Understand the meaning of each column in a
multidigit number (N.B1.K1)
*Translate between different representations
(concrete, pictorial, symbolic) of quantities
(A.B3.K1)
*Understand addition and subtraction algorithms
(N.B4.K1)
*Explore negative numbers in a variety of contexts |
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What does multiplication mean?
What are the basic multiplication facts?
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Products
and Factors
Using Data to Predict |
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*Explore multiplication through rectangular arrays
(N.B2.K5a)
*Explore multiples, prime numbers, and square
numbers (N.B1.K1).
*Find products of more than two factors (N.B4.K7)
*Use factor trees to factor numbers into primes
(N.B4.K7)
*Solve number puzzles that involve the words
multiple, factor, and prime and square numbers
*Use exponents to write products of repeated factors
*Recognize that there are many strategies for doing
simple multiplication problems (N.B4.K1)
*Use efficient strategies to do multiplication
problems (N.B4.A1)
*Use patterns in graphs to make predictions about
data (D.B2.K1)
*Draw a best-fit line
*Investigate the concept of averages (D.B2.A2e)
*Find the mean, median, and mode of a data
set (D.B2.A2d/e)
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How can we make predictions based on patterns in tables and
graphs?
Why is it important to read and write large numbers? |
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Using
Data to Predict (continued)
Place Value Patterns |
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*Measure length (G.B2.A1)
*Identify and use variables in an experiment (A.B2.K2)
*Use patterns in tables and graphs to make
predictions about data (D.B2.A1g/h)
*Work together to solve a problem
*Look back to examine the reasonableness of a
solution (N.B1.A2a)
*Persist in the problem-solving process
*Communicate problem-solving strategies
*Assess concepts and skills developed since the
beginning of the year
*Read large numbers (N.B1.K1a)
*Write large numbers (N.B1.K1a)
*Order large numbers (N.B1.K2a)
*Investigate big numbers (N.B1.A1a)
*Use diagrams to solve problems
*Use patterns in data tables to solve problems
*Use patterns in our base-ten system to visualize
the relative magnitudes of larger numbers
*Construct proportional models to extend base-ten
pieces to 1,000,000
*Link the powers of 10 to the place value system
*Construct a proportional number line for numbers to
1 million
*Place benchmark numbers on a number line for big
numbers (1000 to 1 million)
*Use benchmark numbers to position numbers between
1000 and 1 million
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Objective/Skill continued-
*Use patterns in our base-ten system to visualize
the relative magnitudes of larger numbers
*Estimate the number of objects in a collection
(N.B3.K1)
*Estimate 10% of a number (N.B3.K1)
*Use 10% as a standard for error analysis
*Use benchmarks to round numbers
*Recognize a number can be rounded in many ways
*Estimate sums and differences of large numbers
(N.B3.K2)
*Use paper and pencil to find sums and differences
of larger numbers (N.B4.K1)
*Know efficient strategies to use in problem solving
(N.B3.A4)
*Recognize that there are many strategies for doing
simple multiplication problems (N.B4.A2)
*Use efficient strategies to do multiplication
problems involving 5 and 9 (N.B4.K2) |
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Why
should we learn strategies for doing multiplication?
Why is important to be able to estimate with
multiplication? |
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Patterns
in Multiplication
Measurement |
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*Use the conventional order of operations
*Identify and describing patterns in the multiples
of 2, 3, 5, 6, 9, and 10
*Explore the inverse relationship between
multiplication and division (N.B4.K6c)
*Recognize that there are many strategies for doing
simple multiplication problems (N.B4.A2)
*Use efficient strategies to do multiplication
problems involving the last six facts (N.B4.A2)
*Use the calculator efficiently in problem solving
*Communicate problem-solving strategies
*Understand multiplication as repeated addition (N.B4.K6b)
*Discover patterns when multiplying a one-digit
number by numbers that end in zeros
*Use an unknown in a number sentence (A.B2.A1)
*Understand and use a multiplication algorithm
(N.B1.A1c)
*Know when, how, and why estimation is used
(N.B3.K3)
*Explore different ways of finding and using
convenient numbers
*Multiply multidigit numbers that end in zeros
*Estimate products (N.B3.K1)
*Understand the concept of volume (G.B2.K2b)
*Use appropriate units for measuring volume (G.B2.K2b)
*Measure volume by displacement
*Estimate volume (G.B2.K2b/3)
*Collecting and organizing data (D.B2.K1a/d)
*Graph data using a point graph (D.B2.K1h)
*Use patterns in tables and graphs to make
predictions about data (D.B2.A1d)
*Communicate the solution to a problem |
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Why is communication in math important?
Why should we learn to work in cooperative groups?
Why is it important to know about the different
shapes and solids? |
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Measurement
Shapes and Solids |
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*Solve problems in cooperative groups
*Communicate problem-solving strategies
*Collect and use data to solve problems (D.B2.A1a-h)
*Solve problems involving multiplication and
division (N.B4.K3b/c/d/e)
*Assess concepts and skills developed since the
beginning of the year
*Compare and contrast the following elements of
different labs:
-variables (A.B2.K1)
-measurement procedures (G.B2.A2)
-number of trials
-types of graphs (D.B2.A3)
-problems solved
*Reviewing portfolios
*Reflecting on one's own work
*Identify lines, line segments, rays, and points
*Investigate parallel and perpendicular lines
*Investigate angles
*Measure angles with a protractor
*Identify turn (rotational) symmetry (G.B3.K2)
*Identify line (reflective) symmetry (G.B3.K2)
*Explore two and three dimensions (G.B3.K3)
*Make nets for solids
*Make solids from nets
*Visualize a three-dimensional shape from a
two-dimensional net
*Investigate properties of prisms
*Draw three-dimensional shapes
*Find the volume of prisms
*Construct a geometric solid (G.B1.A1b)
*Identify faces, edges, and vertices of a solid
*Describe a regular solid
*Construct a net |
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| Why is it important to learn how to read and write decimals? |
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Using
Decimals
Multiplication |
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*Measure lengths in metric units (mm, cm, dm, and m) (G.B2.A1b)
*Link the base-ten pieces model for decimals with a
number line model (meterstick)
*Determine which unit of measure for length in most
appropriate in a given context (G.B2.A2)
*Write and read decimals through hundredths
(N.B1.K1c)
*Establish connections between concrete, pictorial,
verbal, and symbolic representations of decimals
(N.B1.K1c)
*Link common fractions and decimals
*Write decimals to the tenths place (N.B1.K1c)
*Write decimals to the hundredths place (N.B1.K1c)
*Identify variables that need to be controlled in an
experiment
*Measure to the nearest hundredth of a meter (G.B2.K2a)
*Use patterns in graphs to make predictions
*Order decimals (N.B1.K2c)
*Identify larger and smaller decimal fractions in
relationship to each other (N.B1.K2b)
*Identify the relationship between a common and a
decimal fraction
*Find 10% of various quantities
*Measure to the nearest tenth of a centimeter (G.B2.K2a)
*Multiply by ten and by one-tenth (N.B4.K2)
*Model multiplication (N.B4.K3)
*Multiply by multiples of ten
*Estimate products (N.B3.K1)
*Use unknowns in multiplication sentences
(A.B2.A2b)
*Compute products using the all-partials method |
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| Why is it important to know how to use different methods to
multiply multidigit by multidigit numbers? |
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Multiplication
Exploring Fractions |
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*Model multiplication with base-ten pieces (N.B1.A1c)
*Use the all-partials method to multiply one-digit
by multidigit numbers
*Estimate products (N.B3.A3)
*Visualize products (N.B3.A3)
*Multiply using the compact method
*Connect multiplication models to the all-partials
method
*Use the all-partials method to compute two-digit by
two-digit multiplication problems
*Multiply two-digit by two-digit numbers using the
compact method
*Understand that other number systems exist and
contributed to the development of our system
*Recognize key elements of the Hindu-Arabic system
*Recognize and using patterns to calculate (N.B4.K1)
*Identify fractional parts of a whole (N.B1.K1b)
*Compare the size of fractions using a physical
model (N.B1.K1b)
*Add and subtract fractions with like denominators
(N.B4.K3f)
*Compare fractions (N.B1.K2b)
*Recognize equivalent fractions |
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Why should we be able to recognize fractions and the wholes they
represent?
What is a fraction?
When are fractions used? |
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Exploring
Fractions
Division |
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*Write equivalent fractions
*Represent fractions using manipulatives and symbols
(N.B1.A2b)
*Find a fraction for a given quantity when a unit
whole is given
*Identify the unit whole when a fraction is given
*Order fractions (N.B1.K2b)
*Use manipulatives to add fractions
*Use pattern blocks to show different fractions
*Work cooperatively to solve a problem
*Communicating problem-solving strategies
*Write number sentences to represent solutions
*Plan and conduct a survey
*Collect, organize, graph, and analyze data
*Bin data
*Use multiplication and division to solve problems
involving time (A.B2.K2c)
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How does division relate to multiplication?
What do we do with the leftover parts after
dividing? |
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*Model division (N.B3.K3e)
*Connect the symbols with division situations
(N.B4.K5)
*Use the forgiving method
for division
*Explore the meaning of remainders
*Model division using the base-ten pieces
*Estimate quotients (N.B3.A2)
*Interpret remainders
*Solve problems involving multiplication and
division (N.B4.A1)
*Choose appropriate methods of computation (N.B4.A1)
*Measure length in cm (G.B2.K2a)
*Collect data over time
*Identify the manipulated, responding, and fixed
variables in an experiment |
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