Math Expressions Grade 2 – Scope and Sequence

MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 1: UNDERSTANDING ADDITION AND SUBTRACTION

Resources: Math Expressions

Estimated Timeframe: 15-‐25 days

Algebra & Functions: ● Solve addition equations with sums through 20 using the commutative property (5+3=8, 3+5=8). ● Solve addition equations with three addends through sums of 20 using the associative property of addition. ● Demonstrate the ability to use a variety of strategies to solve equations and inequalities. ● Recognize, describe, extend, and represent a variety of patterns based on attributes, number, geometry (number patterns, patterns on the calendar, shape patterns, etc.). ● Use addition and subtraction within 100 to solve one-‐ and two-‐step problems with unknowns in all positions. ● Use a strategy (using numbers, symbols (+ -‐), words and/or pictures) to solve addition and subtraction word problems and be able to clearly explain one’s thinking to others.

Number, Number Systems, and Number Relationships: ● Count by 1’s, 2’s, 5’s and 10’s to 1,000. ● Read and write whole numbers to 999 by dictation, using pictures and number names. ● Read and write whole numbers to 999 by dictation, using base-‐ten numerals or from expanded form. ● Use addition and subtraction within 100 to solve one-‐ and two-‐step word problems with unknowns in all positions.

Problem Solving and Communication: ● Use a strategy (using numbers, words and/or pictures) to solve addition and subtraction word problems and be able to clearly explain one’s thinking to others. ● Use grade appropriate mathematical vocabulary such as addition, subtraction, minus, sum, difference, congruent, symmetry, equal, greater than, and less than when solving problems.

Reasoning and Connections: ● Use pictures, words, and/or numbers to clearly express mathematical thinking and to compare solutions and strategies. ● Use words to express mathematical thinking to compare solutions and strategies (e.g., all, or, every, some, or many.)

Supplemental Investigations Activities MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

Mathematical Thinking in 2nd Grade: 1st Edition ● Tens Go Fish (pg. 26) ● Turn Over 10 (pg. 28) ● Collect 25 (pg. 86) ● Counting Strips (pg. 92) ● Collecting Pocket Data (pg. 113) ● How Many Pockets? (pg. 127)

Putting Together and Taking Apart: 1st Edition ● Combining and Separating (pgs. 4-‐34) (Math Talk Resource) ● Cover Up (pg. 74)

Coins, Coupons, and Combinations: 1st Edition ● Ways to Make 15 cents (pg. 76) ● Doubles (pg. 22) ● Counting Bags (pg. 70) ● Magic Pot (pg. 45)

Investigations 2 Resource Binder ● Ten-‐ Frame Cards (Unit 3 M3) ● Addition Cards, Doubles +1 (Unit 3 M16) ● Addition Cards, +10 Combinations (Unit 3 M35) ● +9 or 10 Bingo (Unit 8 M10-‐M11)

Other Supplemental Resources MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 2: MEASUREMENT AND SHAPES

Resources: Math Expressions

Estimated Timeframe: 3-‐5 days -‐ *Could choose to do Unit 2 and Unit 4 sequentially then Unit 3.*

Geometry: ● Using Geoblocks, pattern blocks, colored tiles, etc. name, describe and draw/build 2-‐and 3-‐dimensional shapes (rectangle, square, triangle, rectangular prism, cube, etc.). ● Sort objects by given attributes (size, color, number of sides, edges, etc.).

Measurement and Estimation: ● Measure objects using various tools (rulers, yardsticks, meter sticks, tape measure, scales, thermometers, etc.). ● Use addition and subtraction when comparing different lengths. ● Find perimeter and area using non-‐standard units with teacher assistance.

Supplemental Investigations Activities

Mathematical Thinking in 2nd Grade: 1st Edition ● Find the Blocks (pg. 54-‐60) ● Ways to Fill (pg. 54-‐60) ● Cover and Count (pg. 64-‐67) Shapes, Halves, and Symmetry: 1st Edition (all lessons support geometry objectives) ● Shapes Around Us (pg. 5) ● Seeing Shapes Within Shapes (pg. 14) ● Investigating Quadrilaterals (pg. 46) ● Which Rectangle is Biggest? (pg. 52) ● Building Rectangles (pg. 55) How Long? How Far? 1st Edition ● Investigation 1 (pg. 2-‐43)

Other Supplemental Resources

Elementary Algebra Resource: Grade 1-‐2 ● Sorting Shapes (pg. 5)

UNIT 3: SOLVING STORY PROBLEMS

Resources: Math Expressions

Estimated Timeframe: 14-‐22 days MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

Algebra & Functions: ● Solve addition equations with sums through 20 using the commutative property (5+3=8, 3+5=8). ● Solve addition equations with three addends through sums of 20 using the associative property of addition. ● Demonstrate the ability to use a variety of strategies to solve equations and inequalities. ● Use addition and subtraction within 100 to solve one-‐ and two-‐step problems with unknowns in all positions. ● Use a strategy (using numbers, symbols (+ -‐), words and/or pictures) to solve addition and subtraction word problems and be able to clearly explain one’s thinking to others.

Number, Number Systems, and Number Relationships: ● Count by 1’s, 2’s, 5’s and 10’s to 1,000. ● Identify 1, 2, and 3-‐digit odd or even numbers. ● Use addition and subtraction within 100 to solve one-‐ and two-‐step word problems with unknowns in all positions.

Supplemental Investigations Activities

Coins, Coupons,and Combinations: 1st Edition ● Close to 20 (pg. 39) ● Beat the Calculator (pg. 39) ● Today’s Number (pg. 45) ● Ways to Make 25 (pg. 80) ● Collect 50 Cents (pg. 81) ● Sharing and Developing Strategies (pg. 90-‐107) ● Penny a Pocket (pg. 121)

Putting Together and Taking Apart: 1st Edition MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

● Get to 100 (pg. 45) ● Roll a Square (pg. 49) (also Unit 6 M16-‐17 Investigations 2 Resource Binder) ● 100s Chart (pg. 52) ● Patterns on the 100s Chart (pg. 52) ● Pinching Paper Clips (pg. 61)

Investigations 2 Resource Binder ● Guess My Number on the 100 Chart Unit 6 M8

Other Supplemental Resources

Elementary Algebra Resource: Grade 1-‐2 ● Even Numbers (pg. 21) ● Odd Numbers (pg. 22) ● Skip Counting (pg. 23-‐26, 28) MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 4: TRIANGLES AND QUADRILATERALS

Resources: Math Expressions

Estimated Timeframe: 3-‐5 days -‐ *Could choose to do Unit 2 and Unit 4 sequentially then Unit 3.*

Measurement and Estimation: ● Measure objects using various tools (rulers, yardsticks, meter sticks, tape measure, scales, thermometers, etc.). ● Find perimeter and area using non-‐standard units with teacher assistance.

Supplemental Investigations Activities

Other Supplemental Resources MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 5: ADDITION TO 200

Resources: Math Expressions

Estimated Timeframe: 15-‐20 days

Calculus: ● Order a set of whole numbers from least to greatest or greatest to least up through 999.

Computation & Estimation: ● Use various strategies to develop fluency such as: fact families, doubles, doubles + 1, doubles + 2, doubles -‐ 1, doubles -‐ 2, etc. ● Solve addition and subtraction combinations through 20. ● Add and subtract single and double-‐digit numbers with and without regrouping using both vertical and horizontal notation. ● Use the dollar sign and decimal point OR cents sign when adding and subtracting. ● Demonstrate fluency in using the U.S. Algorithm: ● 2-‐digit Addition & Subtraction with regrouping ● 3-‐digit and 4-‐digit Addition & Subtraction without regrouping ● Multiplication equations using factors from 0 through 5 ● Estimate values, sums, and differences of quantities and determine the reasonableness of those estimates. ● Introduce rounding 2-‐digit numbers to the nearest ten.

Measurement and Estimation ● Find perimeter and area using non-‐standard units with teacher assistance.

Number, Number Systems, and Number Relationships: ● Count by 1’s, 2’s, 5’s and 10’s to 1,000. ● Compare 2-‐ and 3-‐digit whole numbers using >, =, < symbols up through 999. ● Read and write whole numbers to 999 by dictation, using pictures and number names. ● Identify and state the value of the quarter, dime, nickel, and penny. ● Count combinations of coins up to $1.00. ● Read and write whole numbers to 999 by dictation, using base-‐ten numerals or from expanded form. ● Identify 1, 2, and 3-‐digit odd or even numbers. MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

Supplemental Investigations Activities

Putting Together and Taking Apart: 1st Edition ● Problems with a Missing Part (pg. 77-‐85) ● Ways to Make 100 (pg. 96) ● Collect One Dollar (pg. 66) ● Capture 5 (pg. 112) ● Strategies for Combining (pg. 104-‐111, 118-‐122) ● Strategies for Separating (pg. 128-‐134)

Investigations 2 Resource Binder ● Unroll a Square (Unit 6 M32-‐ M34) ● 200 Chart (Unit 6 M7)

Other Supplemental Resources

Nimble with Numbers: 2nd and 3rd Grades ● Addition (pg. 97-‐118) ● Place Value (pg. 73-‐96)

Elementary Algebra Resource: Grade 1-‐2 ● Skip Counting (pg. 27) MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 6: TIME

Resources: Math Expressions

Estimated Timeframe: 4-‐7 days

Algebra & Functions: ● Recognize, describe, extend, and represent a variety of patterns based on attributes, number, geometry (number patterns, patterns on the calendar, shape patterns, etc.).

Measurement and Estimation: ● Project dates on a monthly calendar (e.g., On what day of the week will June 15th be?) ● Read and represent time to the nearest 5 minutes on an analog and digital clock. ● Use the terms quarter after, quarter of the hour, and half-‐past. rd ● Find elapsed time to increments of 5 minutes (limited to 2 adjacent hours)-‐3 Grade indicator

Supplemental Investigations Activities

Other Supplemental Resources

● LEAD-‐ Staff Resources-‐ Elementary Curriculum Docs-‐1/2 -‐ Math-‐ Grade 2-‐ Invest Modules-‐ Telling Time MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 7: TABLES AND GRAPHS

Resources: Math Expressions

Estimated Timeframe: 10-‐15 days (combine lessons as needed)

Algebra & Functions: ● Describe, compare, and answer questions about data on classroom graphs and charts.

Computation & Estimation: ● Add and subtract single and double-‐digit numbers with and without regrouping using both vertical and horizontal notation. ● Add and subtract 3-‐ and 4-‐digit numbers without regrouping using both vertical and horizontal notation.

Number, Number Systems, and Number Relationships: ● Count by 1’s, 2’s, 5’s and 10’s to 1,000.

Probability and Predictions: ● Ask and answer questions about predictions and actual outcomes based on data.

Statistics & Data Analysis: ● Gather, organize, display, compare, and analyze data from surveys collected from school or at home. ● Gather, organize, display, compare, analyze, and communicate data using representations such as pictures, tallies, charts, bar graphs, and pictographs. ● Describe data displayed in a diagram, graph, table, or pictograph. ● Analyze representations of data and compare the data from two categories (such as pictures, tallies, charts, bar graphs, and pictographs, using most, least, more than, less than, equal to). ● Identify patterns and predict trends based on a comparison to data displayed in a graph.

Supplemental Investigations Activities

Mathematical Thinking in 2nd grade: 1st Edition ● Guess my Rule (pg. 102) MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

Does it Walk, Crawl, or Swim?: 1st edition ● Investigation 1 (pgs. 4-‐35)

Other Supplemental Resources

UNIT 8: DIAGONALS AND MIDPOINTS

Resources: Math Expressions

Estimated Timeframe: 0-‐3 days. Can skip entire unit because objectives are not any of the second grade indicators.

UNIT 9: SUBTRACTING 2-‐DIGIT NUMBERS

Resources: Math Expressions

Estimated Timeframe: 15-‐20 days

Algebra & Functions: ● Solve addition equations with sums through 20 using the commutative property (5+3=8, 3+5=8). ● Solve addition equations with three addends through sums of 20 using the associative property of addition. ● Demonstrate the ability to use a variety of strategies to solve equations and inequalities. ● Use addition and subtraction within 100 to solve one-‐ and two-‐step problems with unknowns in all positions. ● Use a strategy (using numbers, symbols (+ -‐), words and/or pictures) to solve addition and subtraction word problems and be able to clearly explain one’s thinking to others.

Computation & Estimation: ● Use various strategies to develop fluency such as: fact families, doubles, doubles + 1, doubles + 2, doubles -‐ 1, doubles -‐ 2, etc. ● Solve addition and subtraction combinations through 20. ● Add and subtract single and double-‐digit numbers with and without regrouping using both vertical and horizontal notation. ● Add and subtract 3-‐ and 4-‐digit numbers without regrouping using both vertical and horizontal notation. ● Use the dollar sign and decimal point OR cents sign when adding and subtracting. ● Demonstrate fluency in using the U.S. Algorithm: ● 2-‐digit Addition & Subtraction with regrouping ● 3-‐digit and 4-‐digit Addition & Subtraction without regrouping ● Multiplication equations using factors from 0 through 5 ● Estimate values, sums, and differences of quantities and determine the reasonableness of those estimates. ● Introduce rounding 2-‐digit numbers to the nearest ten.

Number, Number Systems, and Number Relationships: MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

● Count by 1’s, 2’s, 5’s and 10’s to 1,000. ● Identify and state the value of the quarter, dime, nickel, and penny. ● Count combinations of coins up to $1.00. ● Make change using coins up to $1.00

Supplemental Investigations Activities

*see units 1, 3, and 5

Other Supplemental Resources

Nimble with Numbers: Grades 2 and 3 ● 2-‐Digit Subtraction (pg. 119-‐144)

UNIT 10: SHAPES AND PATTERNS

Resources: Math Expressions

Estimated Timeframe: 5 days

Algebra & Functions: ● Recognize, describe, extend, and represent a variety of patterns based on attributes, number, geometry (number patterns, patterns on the calendar, shape patterns, etc.).

Measurement and Estimation: ● Find perimeter and area using non-‐standard units with teacher assistance. MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

Supplemental Investigations Activities

Shapes, Halves and Symmetry: 1st edition ● Investigation 4 (pgs. 94-‐115)

Other Supplemental Resources MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 11: 3-‐DIGIT ADDITION AND SUBTRACTION

Resources: Math Expressions

Estimated Timeframe:

Algebra & Functions: ● Solve addition equations with sums through 20 using the commutative property (5+3=8, 3+5=8). ● Solve addition equations with three addends through sums of 20 using the associative property of addition. ● Demonstrate the ability to use a variety of strategies to solve equations and inequalities. ● Use addition and subtraction within 100 to solve one-‐ and two-‐step problems with unknowns in all positions. ● Use a strategy (using numbers, symbols (+ -‐), words and/or pictures) to solve addition and subtraction word problems and be able to clearly explain one’s thinking to others.

Calculus: ● Order a set of whole numbers from least to greatest or greatest to least up through 999.

Computation & Estimation: ● Use various strategies to develop fluency such as: fact families, doubles, doubles + 1, doubles + 2, doubles -‐ 1, doubles -‐ 2, etc. ● Solve addition and subtraction combinations through 20. ● Add and subtract single and double-‐digit numbers with and without regrouping using both vertical and horizontal notation. ● Add and subtract 3-‐ and 4-‐digit numbers without regrouping using both vertical and horizontal notation. ● Use the dollar sign and decimal point OR cents sign when adding and subtracting. ● Demonstrate fluency in using the U.S. Algorithm: ● 2-‐digit Addition & Subtraction with regrouping ● 3-‐digit and 4-‐digit Addition & Subtraction without regrouping ● Multiplication equations using factors from 0 through 5 ● Estimate values, sums, and differences of quantities and determine the reasonableness of those estimates. ● Introduce rounding 2-‐digit numbers to the nearest ten.

Number, Number Systems, and Number Relationships: ● Count by 1’s, 2’s, 5’s and 10’s to 1,000. ● Compare 2-‐ and 3-‐digit whole numbers using >, =, < symbols up through 999. ● Read and write whole numbers to 999 by dictation, using pictures and number names. ● Represent a given amount of money in 3 or more ways (up to 1 dollar) using quarters, dimes, nickels, and pennies. ● Identify and state the value of the quarter, dime, nickel, and penny. ● Count combinations of coins up to $1.00. ● Show various combinations of a given amount up to $1.00 using a quarter, dime, nickel, and penny. ● Make change using coins up to $1.00 ● Read and write whole numbers to 999 by dictation, using base-‐ten numerals or from expanded form. ● Identify 1, 2, and 3-‐digit odd or even numbers. ● Use addition and subtraction within 100 to solve one-‐ and two-‐step word problems with unknowns in all MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

positions.

Supplemental Investigations Activities

*see units 1, 3, and 5 *3rd Grade Investigations (see 3rd grade teacher and/or Instructional Coach) ● Close to 100

Other Supplemental Resources MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 12: METRIC MEASUREMENT AND 3-‐D SHAPES

Resources: Math Expressions

Estimated Timeframe: 5 days **Need to cover standard units of measure as part of the second grade curriculum-‐inches, feet, cup, pint, quart, pound-‐using additional resources

Geometry: ● Using Geoblocks, pattern blocks, colored tiles, etc. name, describe and draw/build 2-‐ and 3-‐dimensional shapes (rectangle, square, triangle, rectangular prism, cube, etc.).

Measurement and Estimation: ● Measure objects using various tools (rulers, yardsticks, meter sticks, tape measure, scales, thermometers, etc.) ● Estimate and measure objects to the nearest inch and foot using a ruler. ● Use addition and subtraction when comparing different lengths.

Supplemental Investigations Activities

* see units 2 and 4

Other Supplemental Resources MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 13: MULTIPLICATION AND FRACTIONS

Resources: Math Expressions

Estimated Timeframe: 8-‐14 days (Can skip Lesson 13)

Computation & Estimation: ● Demonstrate fluency in using the U.S. Algorithm: ● 2-‐digit Addition & Subtraction with regrouping ● 3-‐digit and 4-‐digit Addition & Subtraction without regrouping ● Multiplication equations using factors from 0 through 5 ● Use manipulatives and write corresponding multiplication equations as repeated addition.

Geometry: ● Identify and draw designs with symmetry

Number, Number Systems, and Number Relationships: ● Divide whole objects into 2, 3, or 4 equal shares. Describe the shares using the words halves, thirds, half of, a third of, fourth, a fourth of. Describe the whole as two halves, three thirds, four fourths. ● Given a shaded figure (halves, thirds, or fourths) write its corresponding fraction. ● Given a fraction (halves, thirds, or fourths) shade a figure that represents that fractional part. ● Use repeated addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns (using manipulatives or picture representations). ● Use manipulatives and write multiplication equations for a given group of equal sets to products of 25 (factors 0-‐5).

Probability and Predictions: ● Determine if mathematical situations are fair, unfair, likely, unlikely, or certain (e.g., spinners, likely or unlikely statements, and probability games, etc. using the vocabulary: unfair/fair, unlikely/likely, certain, impossible. ● Predict if different outcomes of the same event are equally likely or not equally likely. ● Write the likelihood of an event as a simple fraction (e.g., ½). ● List or graph the possible results of an experiment (spinners and probability games). ● Ask and answer questions about predictions and actual outcomes based on data.

Supplemental Investigations Activities

Shapes, Halves and Symmetry: 1st Edition ● Cube Buildings (pgs. 39-‐40)

Other Supplemental Resources

● LEAD-‐ Staff Resources-‐ Elementary Curriculum Docs-‐1/2 -‐ Math-‐ Grade 2-‐ Invest Modules-‐ Probability MATH EXPRESSIONS GRADE 2 – SCOPE AND SEQUENCE

UNIT 14: NON-‐STANDARD AND STANDARD UNITS OF MEASURE

Resources: Math Expressions

Estimated Timeframe: 2-‐5 days

Measurement and Estimation: ● Estimate and measure objects to the nearest inch and foot using a ruler. ● Estimate and measure liquids to the nearest cup, pint, and quart using various tools and containers. ● Estimate and measure objects to nearest pound.

Supplemental Investigations Activities

* see unit 2

Other Supplemental Resources