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Mathematics Scope and Sequence
Grades K-2

Pennsylvania Content Standards – Mifflin County Benchmarks
Completed April 18, 2001

2.1 Numbers, Number Systems, and Number Relationships
	K	1	2
A.	1. Count using whole numbers to 20 by ones. 2. Skip count by multiples of 10 to 100.	Count by 1’s, 5’s, 10’s to 100.	Count using whole numbers to 1,000.
A.		Count backwards from 20 to 0 orally and in written form.	Count by 2’s and 3’s to 100.
B.	Use whole numbers up to 20 to represent quantities.	Recognize and color ½, 1/3, and ¼ of a set, object, or shape.	Interpret whole numbers and fractions which represent quantities.
C.	1. Represent the numbers 1 through 10 using concrete objects. 2. Represent the numbers 1 through 10 using drawings. 3. Represent the numbers 1 through 10 using symbols. 4. Write numerals 0-20.D. Recognize equal parts and identify ½ of an object or shape.	1. Recognize numbers to 100. 2. Write numbers to 100.
D.		Recognize and color ½, 1/3, and ¼ of a set, object, or shape.	Equate correct number of fractional parts to a whole number using concrete objects, drawings, and word names.
E.		1. Match the name and value (cent sign) of a penny, nickel, dime, and quarter. 2. Count a given amount of money up to $1.00 using dimes, nickels, and pennies. 3. Select the correct numbers of dimes, nickels, and pennies to match a given amount of money. 4. Solve money problems using a simulated experience like a school store.	1. Find value of collection of coins for values below one dollar. 2. Compute and record addition and subtraction money problems using cent and dollar symbols with paper and pencils.
F	1. Compare values of numbers up to 10 and identify "more than" and "less than." 2. Correctly use the terms "first," "next," and "last."	1. Compare and order whole numbers to 100. 2. Identify ordinal position of an object (first through tenth). 3. Identify and explain a given pattern on a hundred board.	Use a number board to facilitate counting.
G.	1. Represent the numbers 1 through 10 using concrete objects. 2. Use concrete objects to count and make sets up to 20.		Given any two-digit number to 89, mentally calculate the sum by adding 10.
H.	Use concrete objects to demonstrate understanding of one-to-one correspondence up to 20.
I.		Demonstrate an understanding of place value using manipulatives such as base ten blocks, unifix cubes, dimes, pennies, and pictures.	Write numbers in expanded form.
J.			Estimate quantities to nearest 10 and 100.
K.	Create addition and subtraction problems using manipulatives up to 10.	Create a story problem involving addition or subtraction given a number sequence.
L.		1. Write a four-part number family which includes two addition and two subtraction number sentences. 2. Demonstrate mental proficiency in addition and subtraction facts to 10. 3. Demonstrate an understanding of the value of zero by adding zero to or subtracting zero from a number.	1. 2. Demonstrate mental proficiency in addition and subtraction facts to 18.

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2.2 Computation and Estimation
A.		1. Determine the sum of 2 or 3 addends by writing number sentences. 2. Deduce the difference of any two numbers to 12 without regrouping by using manipulatives or drawing pictures. 3. Deduce the difference of any two numbers to 12 without regrouping by writing number sentences.
B.		Determine the sum of 2 or 3 addends to 12 by using manipulatives or drawing pictures.	1. Add 3 two-digit numbers with and without regrouping. Subtract two-digit numbers with and without regrouping. 3. Add and subtract two-digit numbers mentally without regrouping.
C.
D.
E.	Make estimates of objects.
F.	State a reason for guesses/estimation.		Use estimation to determine reasonableness of answers to addition and subtraction problems up to 1,000.
	Use manipulatives to demonstrate and explain single digit addition of sums to 10.		Describe the computation process used to solve a problem.

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2.3 Measurement and Estimation
A.			Measure, record, and graph temperatures to the nearest 5 degrees.
B.		1. Estimate and measure objects using nonstandard units. 2. Measure, record, and compare the length of familiar objects to the nearest inch and centimeter.	1. Measure to the nearest foot. 2. Draw line segments to inch and centimeter.
C.	Name and order the days of the week.	1. Name and order the months of the year. 2. Locate and report the date (including month, day, and year) on a calendar. 3. Identify yesterday’s, today’s, and tomorrow’s date.	Project the date(s) for the following week.
D.	1.Tell time to the hour using an analog clock. 2. Tell time to the hour using a digital clock.		Read and represent time to the nearest half-hour and 5-minute intervals.
E.
F.			Measure and calculate the perimeter of squares, triangles, and rectangles to the nearest inch.

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2.4 Mathematical Reasoning and Connection

Make and verify predictions about quantity, size, and shape.

1. Use manipulatives or pictures to explain and justify a solution.

2. Estimate an answer and defend its reasonableness.

Verify and defend predictions related to real-life events.

1. Create and solve story problems about real-life events.

2. Write and solve number sentences about real-life events.

3. Extend and solve problems connected to literature, social living, science, and health.

Verify and defend the use of a unit of measure for real-life events.

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2.5 Mathematical Problem Solving and Communication
A.	Create a story problem.	1. Create word problems from real-life situations involving addition or subtraction concepts, then solve. 2. Solve non-routine problems using charts and graphs. 3. Choose correct operation in problem situation.
B.	Explain and justify the process used to arrive at a solution through the use of pictures, diagrams, or manipulatives.	1. Defend a solution to a story problem using manipulatives and/or drawings. 2. Explain and justify the process chosen to develop and solve equations in either addition and/or subtraction.
C.	Explain and justify the process used to arrive at a solution through the use of pictures, diagrams, or manipulatives.	Defend a solution to a story problem using manipulatives and/or drawings.

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2.6 Statistics and Data Analysis
A.	1. Read, organize, and compare real-life data on a bar graph and/or pictograph using the following vocabulary: most, least, same, highest, lowest, more than, fewer than. 2. Create a bar graph and/or pictograph using real-life data.	1. Collect data by observing, counting, measuring, and tallying. 2. Organize and compare data using bar graphs and/or pictographs.
B.	Interpret and describe analysis of data on a given graph.	Describe, interpret, and compare data from bar graphs, pictographs, and line plots utilizing information gathered from graphs.

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2.7 Probability and Predictions
A.	State the likelihood of a chance event, and explain your reasoning using the following vocabulary: likely, unlikely, and certain.
B.		Gather data using a spinner and other manipulatives, and record data using tallies.
C.		Describe, interpret, and compare data using basic probability concepts and the phrases "equally often," "less often," and "impossible."

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2.8 Algebra and Functions
A.	Recognize, describe, extend, and replicate patterns.	Identify, continue, and orally describe a simple number or shape pattern.	Identify, describe, and extend repeating and continuing shapes and number patterns.
B.		Use concrete objects and trial and error to create number sentences.	Solve number sentences using concrete objects.
C.		Use manipulatives to determine a missing addend in a number sentence in which the sum is 10 or less.
D.		Create and solve simple story problems using number sentences and drawing pictures.	Demonstrate, solve, and describe story problems using addition and/or subtraction equations.
E.			Use and interpret symbols to show addition and subtraction.
F.
G.
H.			Analyze and interpret data shown in tables and charts.
I.
J.			Locate points on a simple grid.

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2.9 Geometry
A.	1. Identify four basic two-dimensional shapes (circle, square, rectangle, and triangle). 2. Name four basic two-dimensional shapes (circle, square, rectangle, and triangle).		Classify and name two-and three-dimensional figures by attributes.
B.
C.		1. Construct a triangle, rectangle, and square using a geoboard, and reproduce the figure on grid paper. 2. Identify the number of corners in a square and a rectangle.	1. Draw and compare common geometric shapes including square, rectangle, triangle, and circle. 2. Recognize and draw congruent line segments. 3. Discriminate between open and closed figures.
D.	Identify the number of sides on a square and a rectangle.
E.		Demonstrate a knowledge of the concept of left and right.	Identify and draw lines of symmetry.
F.
G.
H.		Cover a design using pattern blocks.
I.		Count the number of pattern blocks used to cover a pattern.	Count the number of pieces required to cover designs using tangrams.

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2.10 Trigonometry
A.			Identify and give examples of right angles in real-life objects.
B.	Identify the number of sides on a triangle.	Identify the number of corners in a triangle.	Identify parallel and perpendicular lines in real-life objects.

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2.11 Concepts of Calculus
A.	Identify least and greatest values represented in a bar graph or a pictograph up to 10.	1. Order whole numbers from least to greatest between 1 and 100. 2. Compare numbers by identifying most, fewest, more, less, and how many more or less in a set.	1. Place numbers in order from least to greatest and vice versa to 200. 2. Use symbols to depict greater than and less than.
B.		Use a pictograph to compare and identify "most," "least," and "none."	Identify the least and greatest values from information presented on bar graphs and pictographs.
C.
D.			Identify, describe, and extend repeating and continuing number patterns.

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Mathematics Scope and Sequence Grades K-2

Mathematics Scope and Sequence
Grades K-2