Ravalli County Curriculum Consortium

Mathematics

K-8

Ravalli County Curriculum Consortium

Mathematics K-8

Mathematics Measurement Topics / K / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8

Strand: Numbers Sense and Operations

Numbers and Equivalent Representations / * / * / * / *
Counting / * / * / * / *
Addition/Subtraction / * / * / *
Multiplication/Division / * / * / * / * / * / *
Fractions, Decimals, Percents / * / * / * / * / * / * / * / *
Ratio and Proportion / * / * / *
Scientific Notation / * / * / *
Real Numbers / *
Place Value / * / * / * / * / * / * / * / *
Measurement Units / * / * / * / * / *
Time and Temperature / * / * / * / * / *

Strand: Algebraic and Functional Reasoning

Symbols and Expressions / * / * / * / * / * / * / * / * / *
Equations / * / * / * / * / * / * / * / *
Functions and Relationships / * / * / *
Linear and Non-Linear Equations / * / * / *
Inequalities / * / *
Patterns / * / * / * / * / * / * / * / * / *
Properties / * / * / *

Strand: Geometric Reasoning

Geometric Figures / * / * / * / * / * / * / * / * / *
Congruence and Symmetry / * / * / * / * / * / * / * / * / *
Transformations / * / * / * / * / * / * / *
Geometric Properties / * / * / * / * / * / * / * / * / *
Length, Area and Volume / * / * / * / * / * / * / * / * / *
Capacity and Weight / * / * / * / * / * / * / * / *

Strand: Data Analysis

Data Collection, Organization and Display / * / * / * / * / * / * / * / * / *
Analysis / * / * / * / * / * / * / * / * / *
Probability / * / * / * / * / * / * / * / *

K-2

Strand: Number Sense and Operations
Topic: Numbers and Equivalent Representations
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• recognizes numbers from 0 -10 in random order.
The student exhibits no major errors or omissions. /
• Students will state the names of random numbers given to them in various forms (e.g. counters, number cards).

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• recognizes numbers from 0 – 10, in numeric order.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Given a prompt of a number line, students will state the name of a given number.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Topic: Numbers and Equivalent Representations
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• read, write (in standard form), compare and order numbers from 0 – 100
• recognize ordinal positions first through tenth
The student exhibits no major errors or omissions. /
• On a given number line (1-100), student follow verbal directions to place markers on appropriate number, to illustrate understanding of skills such as greater or less than, before and after and between.
• Students form a physical line using ten students and are able to verbalize an indicated position.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• identifies ordinal positions first through fifth
• reads, writes, compares and order numbers from 0-50
• recognizes or recalls basic terminology such as:ordinal position
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Given a picture with 5 objects, students can verbalize which object is in first, second, third position etc.
• On a given number line (1-50), student follow verbal directions to place markers on appropriate number, to illustrate understanding of skills such as greater or less than, before and after and between.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Topic: Numbers and Equivalent Representations
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• read, write, compare and order numbers 0 – 999
• use ordinal position first through twentieth
The student exhibits no major errors or omissions. /
• On a number line up to 999, circle one number and have students identify what number comes before, after and between the given number(s).
• Students will be given a task of putting 20 objects in a row and writing the ordinal position under each.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• reads, writes, compares and orders numbers 0-500
• uses ordinal position first through twelfth
• recognizes or recalls basic terminology such as:
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• On a number line up to 500, circle one number and have students identify what number comes before, after and between the given number(s).
• Students will be given a task of putting 12 objects in a row and writing the ordinal position under each.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Topic: Counting
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• count to 20 by demonstrating one-to-one correspondence using counters
The student exhibits no major errors or omissions. /
• Verbally count to 20 while moving counters.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• counts to 10 by demonstrating one-to-one correspondence using counters
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Verbally count to 10 while moving counters.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Topic: Counting
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• use number patterns and models to count by 2’s, 5’s, and 10’s to 100
The student exhibits no major errors or omissions. /
• Verbally count to 100 by 2’s.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• uses number patterns and models to count by 2’s, 5’s, and 10’s to 50
• recognizes or recalls basic terminology such as:
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Verbally count to 50 by 5’s.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Topic: Counting
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• Use number patterns and models to count by 3’s to 30 and 4;s to 40.
The student exhibits no major errors or omissions. /
• Identify missing numbers on a number line.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• Students will identify a number pattern when given a set of skip-counted-numbers. i.e. 4, 8, 12, 16.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Given a set of numbers, students will identify the pattern.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• add and subtract one- and two- digit numbers without regrouping
The student exhibits no major errors or omissions. /
• 10 – 8 = ___
• Recall 20 out of 40 facts in one minute (e.g., 0+1=1, 1+1=2, 2+2=4, etc.).

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• add and subtract one digit numbers without regrouping
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Circle the correct answer: 8 or 5
7 - ____ = 2
• Recall 15 out of 40 facts in one minute (e.g.,
0+1=1, 1+1=2, etc.).
1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• add and subtract two and three digit numbers with and without regrouping
The student exhibits no major errors or omissions. /
• Circle the correct answer: 28 or 34
23+_____=51
• Recall 40 addition and subtraction facts in one minute.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• add and subtract 2 digit numbers with or without regrouping
• solves addition and subtraction facts using addends 3s, 4s and 5s
• recognizes or recalls basic terminology such as:
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. / Solve 23+28+51
• Recall 20 out of 40 addition and subtraction facts in one minute.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Topic: Fractions, Percents and Decimals
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• distinguish between a whole object and half an object.
The student exhibits no major errors or omissions. /
• Given pictures of whole and part objects, ask the student to circle the whole objects and to place a square around the part objects.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• Recognize the difference between the whole, and a part.
• whole, part
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• When given a picture of a pie, the students will be able to determine if it is a whole pie, or a partially-eaten one.
• Ask the student to produce or identify definitions to given terms.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Strand: Number Sense and Operations
Topic: Fractions, Percents and Decimals
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• use the unit fractions1/2, 1/3, and ¼ as equal parts of a whole or sets of objects.
The student exhibits no major errors or omissions. /
• Shade in ½, ¼ and 1/3 of a given shape.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• Identifies the shaded area in a given shape.
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Students will match pictures of shaded areas with given fractions.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Number Sense and Operations
Topic: Measurement Units
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• explain hours, inches, pounds and the situations in which each unit is appropriate
The student exhibits no major errors or omissions. /
• Students will be able to match hours with time, inches with distance and pounds with weight and give examples of the best situations to use each measurement

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• recognizes examples of the situation in which hours, inches and pounds are used
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Students will match hours with time, inches with distance and pounds with weight when prompted by a teacher. I.E, “Which one of these would you measure a fish with? How would you measure how long until recess?”

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.
0.5 / With help, a partial understanding of the 2.0 content but not the 3.0 content
Score 0.0 / Even with help, no understanding or skill demonstrated.
Number Sense and Operations
Topic: Measurement Units
Score 4.0 / In addition to Score 3.0, in-depth inferences and applications that go beyond what was taught. / Sample Tasks
3.5 / In addition to score 3.0 performance, in-depth inferences and applications with partial success.
Score 3.0 / The student will:
• use non-standard, standard and metric units (e.g., length (inches and centimeters), time and temperature)
The student exhibits no major errors or omissions. /
• Students will be able to measure the length of a pencil in inches and centimeters.

2.5 / No major errors or omissions regarding 2.0 content and partial knowledge of the 3.0 content
Score 2.0 / There are no major errors or omissions regarding the simpler details and processes as the student:
• recognizes a centimeter and inch on a ruler, a degree on a thermometer and tells time
However, the student exhibits major errors or omissions regarding the more complex ideas and processes. /
• Students will recognize an inch on a ruler, low and high degree on a thermometer and tell time on an analog and digital clock.

1.5 / Partial knowledge of the 2.0 content but major errors or omissions regarding the 3.0 content
Score 1.0 / With help, a partial understanding of some of the simpler details and processes and some of the more complex ideas and processes.