subtract. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. Explain why addition and subtraction strategies work, using place value and the properties of operations.1 1 Explanations may be supported by drawings or objects. 182 + 18 190 10 200 Subtraction across zeros can be done by decomposing the base ten number into 1 and 1 less than the number. For example, 200 – 18. Decompose 200 into 199 + 1. Subtract the 18 from 199 and add the one back on. Module 4: Using Bar Models: Addition and Subtraction one for benchmark assessment) Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a Join Take away Set Compare Visuals: Tape Diagrams Strips Students can build the models with strips of paper before drawing. The strips can be cut from colored stock paper or plain colored paper. Strips can be the whole, halves, thirds, and fourths to have different sizes available.
M.P. 8 Remember mastery is not expected until end of 3rd grade. Module 7: Metric Measurement and Length (9 days) M.P. 1 M.P. 2 M.P. 5 M.P. 6 Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Estimate lengths using units of inches, feet, centimeters, and meters. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length. Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. Meterstick, Meter, Width, Length, Unit, Height, Taller, Tallest, Shorter, Shortest, Longer, Longest, Centimeter, Students should be applying the addition and subtraction strategies they have learned here. If the problem is two digit, reinforce the mental strategies. Metric measurements should reinforce the place value system. Also, introduce the word parts to students, as Module 10: Mental Math and Estimation (11 days) Use place value understanding and properties of operations to add and subtract. Sum Add mentally, Difference, Subtract Number talks with two digit addition and subtraction should be used to help students build mastery of facts
M.P. 1 M.P. 3 M.P. 4 M.P. 6 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Add up to four two-digit numbers using strategies based on place value and properties of operations. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number Explain why addition and subtraction strategies work, using place value and the properties of operations.1 Explanations may be supported by drawings or objects. Represent and solve problems involving addition and subtraction. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. mentally, Number line, About, Round, Nearest ten, Estimate, Reasonable to 20 and combinations of 100. Students need to master the terms sum and difference, and finalize their understanding of breaking up numbers (decomposing) doing the operations and adding or subtracting to compensate. The number line can be a great tool to show students how close a number and relate this to rounding. 59 + 35 can be done with 60 + 35 – 1. 220 + 48 can be done with 220 + 48 (220 + 40 + 8). 715 + 160 can be done thinking 800 + 75 (60 + 15). When the students are subtracting 10, help them see they may have taken away too much and have to add the remaining part of the number back. Tools to help are the number line and bar models.
1See Glossary, page 88 of Common Core Standards. Add and subtract within 20. Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers. Relate addition and subtraction to length. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. Module 11: Money (8 days) Do not forget Common Core Lesson 3.a on Pg. 308A M.P. 1 M.P. 3 M.P. 4 M.P. 6 Work with time and money. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? $1, $5, $10, $20 Bill, Cent sign ¢, Dollar sign $, Decimal point, Table, Reinforce the bar models and mental strategies when possible. Connect the place value to money values. As 230 cents is 200 pennies that is 2 dollars; 30 cents is 3 dimes; $2.30. Another common word that needs to be taught is point – decimal point. Have students brainstorm different ways to use point and draw pictures for them. Include decimal point as one of the uses.
Module 12: Fractions (7 1 day for benchmark assessement) M.P. 1 M.P. 4 M.P. 6 M.P. 7 Reason with shapes and their attributes. Partition a rectangle into rows and columns of squares and count to find the total number of them. Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. Equal, Unequal, Whole, Fraction, One-half, One-third, One-fourth, Unit fraction, Same, Greater than, Less than, Like fractions The importance is to help build to 3rd grade. Key concepts - Identify what the whole is and what a unit fraction is; distinguish between decomposing a shape into equal parts or unequal parts also. Module 13: Customary Measurement of Length (9 days) M.P. 1 M.P. 4 M.P. 5 M.P. 6 Measure and estimate lengths in standard units. Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. Estimate lengths using units of inches, feet, centimeters, and meters. Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Foot/feet, Length, Ruler, Unit, Width, Length, Longest, Shortest, Inch, Students will only work with feet and inches. Use the mental math strategies as much as possible for the arithmetic. The more practice students have measuring, the better they will master the concepts. You may want to incorporate measurement into science at this time.
Models: Multiplication and Division (7 days) M.P. 1 M.P. 6 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. mental strategies for the arithmetic. Even though this is connected to the Relate Addition and subtraction to length, most of the problems with regard to x and ÷ will be mastered in 3rd grade. Module 17: Picture Graphs (8 one day for benchmark assessment) M.P. 1, M.P. 2 M.P. 4, M.P. 6 Represent and interpret data. Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems1 using information presented in a bar graph. Picture graph, Key, Symbol, Record, Tally chart, Line plot Focus on the unit scale. Students can practice their skip counting also. Help students to be organized putting pictures in groups. Again, this is precursor to build multiplication in 3rd grade. Module 18: Lines and Surfaces (5 days) M.P. 1 M.P. 2 M.P. 6 Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Part of a line, Curve, Flat surface, Curved surface, Slide, Stack, Roll It is important to bring in the 3 dimensional terminology of faces. Use angle where appropriate. Module 19: Shapes and Patterns (13 Reason with shapes and their attributes. Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of Plane shape, Hexagon, Trapezoid, Lots of vocabulary in this module. Plane is a common core that has special meaning
3 days for benchmark assessment) M.P. 5 M.P. 6 M.P. 7 M.P. 8 equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. Figure, Quadrilateral, Pentagon, Angle, Face, Pattern, Pattern unit, Size, Turning, Shape in mathematics – 2 dimensional. Key: Major Clusters; Supporting Clusters; Additional Clusters