Represent and Solve Problems Involving Addition and Subtraction

Grade 1 Operations and Algebraic Thinking 1.0A Represent and solve problems involving addition and subtraction. Teaching AVMR Towards Common Core Standard Components of the standard Activities that Support the Standard Support Construc F/P/N* t / Level 1. Use addition and Use addition and subtraction within 20 to none none N subtraction within 20 to solve word problems involving situations of solve word problems adding to, taking from, putting together, involving situations of taking apart, and comparing, with unknowns adding to, taking from, in all positions, e.g., by using objects, putting together, taking drawings, and equations with a symbol for apart, and comparing, with the unknown number to represent the unknowns in all positions, problem.2 e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.2 2. Solve word problems Solve word problems that call for addition of none none N that call for addition of three whole numbers whose sum is less than three whole numbers or equal to 20, e.g., by using objects, whose sum is less than or drawings, and equations with a symbol for equal to 20, e.g., by using the unknown number to represent the objects, drawings, and problem. equations with a symbol for the unknown number to represent the problem. *F is Full; P is Partial; N is None

Understand and apply properties of operations and the relationship between addition and subtraction. AVMR Components of Teaching Towards Activities that Support Common Core Standard Support the standard Construct / Level the Standard F/P/N* © 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. 3. Apply properties of operations as Apply properties Add/Subt. Green Book: F strategies to add and subtract.3 of operations as 5 8.5.1 Building numbers 6 Examples: If 8 + 3 = 11 is known, strategies to add to 10 then 3 + 8 = 11 is also known. and subtract.3 8.5.2 Doubles: 3+3, 4+4, (Commutative property of addition.) Examples: If 8 + 5+5 To add 2 + 6 + 4, the second two 3 = 11 is known, 8.5.3 Building numbers numbers can be added to make a then 3 + 8 = 11 is 11 to 20 ten, so 2 + 6 + 4 = 2 + 10 = 12. also known. 8.5.4 Doubles: 6+6 to (Associative property of addition.) (Commutative 10+10 property of 8.5.5 Doubles plus or addition.) To add minus one 2 + 6 + 4, the 8.5.6 Addition by going second two through 10 numbers can be 8.5.7 Commutativity of added to make a addition ten, so 2 + 6 + 4 = 8.5.8 Addition by 2 + 10 = 12. compensation (Associative 8.5.9 Subtraction by property of going through 10 addition.) Purple Book: A6.1 Additive tasks involving 2 screened collections A6.2 Missing addend task involving 2 screened collections A6.3 Removed items task involving a screened collection A6.4 Missing subtrahend task involving a screened collection A6.5 Comparative subtraction involving 2 screened collections A6.6 Subtraction with bare numbers

4. Understand subtraction as an Understand Add/Subt. Green Book: F © 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. unknown-addend problem. For subtraction as an 5 7.3.4 Removed items example, subtract 10 – 8 by finding unknown-addend tasks the number that makes 10 when problem. For added to 8. example, subtract Purple Book: 10 – 8 by finding A6.1 Additive tasks the number that involving 2 screened makes 10 when collections added to 8. A6.2 Missing addend task involving 2 screened collections A6.3 Removed items task involving a screened collection A6.4 Missing subtrahend task involving a screened collection A6.5 Comparative subtraction involving 2 screened collections A6.6 Subtraction with bare numbers

*F is Full; P is Partial; N is None

Add and subtract within 20. AVMR Components of Teaching Towards Activities that Support Common Core Standard Support the standard Construct / Level the Standard F/P/N* 5. Relate counting to addition and Relate counting to Add/Subt. Purple Book: F subtraction (e.g., by counting on 2 to addition and 3 A6.1 Additive tasks add 2). subtraction (e.g., involving 2 screened by counting on 2 collections to add 2). A6.2 Missing addend task involving 2 screened collections A6.3 Removed items task involving a screened collection A6.4 Missing subtrahend

6. Add and subtract within 20, Add and subtract Structuring 3 Green Book: F demonstrating fluency for addition within 20, 8.5.1 Building numbers 6 and subtraction within 10. Use demonstrating Add/Subt. to 10 strategies such as counting on; fluency for 5 8.5.2 Doubles: 3+3, 4+4, making ten (e.g., 8 + 6 = 8 + 2 + 4 = addition and 5+5 10 + 4 = 14); decomposing a subtraction within 8.5.3 Building numbers number leading to a ten (e.g., 13 – 4 10. Use strategies 11 to 20 = 13 – 3 – 1 = 10 – 1 = 9); using the such as counting 8.5.4 Doubles: 6+6 to relationship between addition and on; making ten 10+10 subtraction (e.g., knowing that 8 + 4 (e.g., 8 + 6 = 8 + 2 8.5.5 Doubles plus or = 12, one knows 12 – 8 = 4); and + 4 = 10 + 4 = 14); minus one creating equivalent but easier or decomposing a 8.5.6 Addition by going known sums (e.g., adding 6 + 7 by number leading to through 10 creating the known equivalent 6 + 6 a ten (e.g., 13 – 4 8.5.7 Commutativity of + 1 = 12 + 1 = 13). = 13 – 3 – 1 = 10 addition – 1 = 9); using the 8.5.8 Addition by relationship compensation between addition 8.5.9 Subtraction by and subtraction going through 10 (e.g., knowing that 8 + 4 = 12, one Purple Book: knows 12 – 8 = 4); A7.1 Naming and and creating visualizing pairwise equivalent but patterns for 1 to 10 easier or known A7.2 Naming and sums (e.g., adding visualizing fivewise 6 + 7 by creating patterns for 1 to 10 the known A7.3 Naming and equivalent 6 + 6 + visualizing pairwise 1 = 12 + 1 = 13). patterns for 11 to 20 A7.4 Naming and visualizing fivewise and tenwise patterns for 11 to © 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. 14 A7.5 Naming and visualizing tenwise patterns for 15 to 20 A7.6 Addition using doubles, fives, and tens – addends less than 11 A7.7 Subtraction using doubles, fives and tens – subtrahend and difference less than 11 A7.8 – Addition using doubles, fives and tens – one addend greater than 10 A7.9 – Subtraction using doubles, fives and tens – subtrahend or difference greater than 10

IA7.l The double decker bus flashes IA7.2 Getting on and off the bus IA7.3 Bus snap IA7.4 Make combinations to twenty fish IA7.5 Using ten plus combinations IA7.6 Five and ten game IA7.7 Chocolate boxes IA7.8 Double ten frame facts IA7.9 Bead board

Work with addition and subtraction equations.

© 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. AVMR Components of Teaching Towards Activities that Support Common Core Standard Support the standard Construct / Level the Standard F/P/N* 7. Understand the meaning of the Understand the none none N equal sign, and determine if meaning of the equations involving addition and equal sign, and subtraction are true or false. For determine if example, which of the following equations equations are true and which are involving addition false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, and subtraction 4 + 1 = 5 + 2. are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2 8. Determine the unknown whole Determine the Addition and subtraction 3, 4 Green Book: F number in an addition or subtraction unknown whole or 5 7.3.1 Counting items in equation relating three whole number in an two screened collections numbers. For example, determine addition or 7.3.2 Counting items in a the unknown number that makes subtraction row with some items the equation true in each of the equation relating screened equations 8 + ? = 11, 5 = � – 3, 6 + three whole 7.3.3 Missing addend 6 = �. numbers. For tasks example, 7.3.4 Removed items determine the tasks unknown number 7.3.5 Missing subtrahend that makes the tasks equation true in 7.3.7 Subtractive tasks each of the equations 8 + ? = Purple Book: 11, 5 = � – 3, 6 + A6.2 Missing addend task 6 = �. involving 2 screened collections A6.4 Missing subtrahend task involving a screened collection

Number and Operations in Base Ten 1.NTB Extend the counting sequence. 1. Count to 120, starting at Count to 120, starting at any number less FNWS Green Book: P any number less than 120. than 120. In this range, 5 6.1.1 Saying Short FNWSs In this range, read and *6.1.2 Saying Short BNWSs write numerals and *6.1.3 Saying Alternate Number Words represent a number of Forwards and Backwards objects with a written 6.1.4 Saying the Next One, Two or Three numeral. Number Word Forwards *6.1.5 Saying the Next One, Two or Three Number Word Backwards 6.1.6 Saying the Number Word After *6.1.7 Saying the Number Word Before 7.1.1 Saying Short FNWSs *7.1.2 Saying Short BNWSs 7.1.3 Saying One, Two or Three Numbers After a Given Number *7.1.4 Saying One, Two or Three Numbers Before a Given Number *7.1.5 Saying the Next One, Two or Three Number Word Backwards

Purple Book: A3.1 Forward Number Word Sequence A3.2 Number Word After A3.7 Sequencing Numerals A3.8 Ordering Numerals IA3.1 Count Around IA3.2 Numbers on the Line IA3.3 Stand in Line IA3.8 Choir Counting

read and write numerals and NID Green Book: P 5 7.2.5 Numeral recognition 7.2.6 Numeral identification 7.2.7 Numeral tracks in range 20 to 100 © 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. 7.2.8 Numeral roll 1 to 100 7.2.9 Hundred square 7.2.10 __Hundred square

represent a number of objects with a written Tens/One None (need to use bundles and sticks with N numeral. s 1 or 2 written numerals)

Understand place value. 2. Understand that the two Understand that the two digits of a two-digit Tens/One Purple Book: F digits of a two-digit number number represent amounts of tens and ones. s 1 or 2 A8.1 Forward and backward number word represent amounts of tens Understand the following as special cases: sequences by 10s, on and off the decade and ones. Understand the a. 10 can be thought of as a bundle of ten A8.2 Adding from a decade and subtracting to following as special cases: ones — called a “ten.” a decade a. 10 can be thought of b. The numbers from 11 to 19 are A8.3 Adding to a decade and subtracting from as a bundle of ten ones composed of a ten and one, two, three, a decade — called a “ten.” four, five, six, seven, eight, or nine ones. A8.4 Incrementing and decrementing by 10s b. The numbers from c. The numbers 10, 20, 30, 40, 50, 60, on and off the decade 11 to 19 are composed 70, 80, 90 refer to one, two, three, four, A8.5 Incrementing flexibly by 10s and ones of a ten and one, two, five, six, seven, eight, or nine tens (and 0 A8.6 Adding 10s to a 2-digit number and three, four, five, six, ones). subtracting 10s from a 2-digit number seven, eight, or nine A8.7 Adding two 2-digit numbers without and ones. with regrouping c. The numbers 10, 20, A8.8 Subtraction involving two 2-digit numbers 30, 40, 50, 60, 70, 80, without and with regrouping 90 refer to one, two, A8.9 Addition and subtraction using three, four, five, six, transforming, compensating, and other seven, eight, or nine strategies tens (and 0 ones). A9.1 Higher decade addition and subtraction without and with bridging the decade A9.2 Partitioning and combining involving 2- digit numbers A9.3 Combining and partitioning involving non-canonical forms A9.4 Addition involving two 2-digit numbers without and with regrouping

© 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. A9.5 Subtraction involving two 2-digit numbers without and with regrouping IA8.1 Leap Frog IA8.2 Bead String with Ten Catcher IA8.3 Add or Subtract 11 IA8.4 Add to or Subtract from 49 IA8.5 Calculator Challenge IA8.6 Jump to 100 IA8.7 Jump from 100 IA8.8 Target Number IA8.9 Walk-about Sequences IA8.10 Non-standard Measurement Plan IA9.1 Follow the Pattern IA9.2 Ten More or Ten Less IA9.3 Counting by Tens IA9.4 Add or Subtract Tens IA9.5 Adding Tens and Ones Using Money IA9.6 Screened Subtraction Tasks IA9.7 Split the Subtrahend (Multiples of 10) 3. Compare two two-digit Compare two two-digit numbers based on none none N numbers based on meanings of the tens and ones digits, meanings of the tens and recording the results of comparisons with the ones digits, recording the symbols >, =, and <. results of comparisons with the symbols >, =, and <. *F is Full; P is Partial; N is None

Use place value understanding and properties of operations to add and subtract. 4. Add within 100, including Add within 100, including adding a two-digit Tens/One Purple Book: F adding a two-digit number number and a one-digit number, and adding s 1 or 2 A8.1 Forward and backward number word and a one-digit number, a two-digit number and a multiple of 10, using sequences by 10s, on and off the decade and adding a two-digit concrete models or drawings and strategies A8.2 Adding from a decade and subtracting to number and a multiple of based on place value, properties of a decade 10, using concrete models operations, and/or the relationship between A8.3 Adding to a decade and subtracting from or drawings and strategies addition and subtraction; relate the strategy a decade based on place value, to a written method and explain the A8.4 Incrementing and decrementing by 10s properties of operations, reasoning used. Understand that in adding on and off the decade and/or the relationship two-digit numbers, one adds tens and tens, A8.5 Incrementing flexibly by 10s and ones between addition and ones and ones; and sometimes it is A8.6 Adding 10s to a 2-digit number and

© 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. necessary to compose a ten subtracting 10s from a 2-digit number A8.7 Adding two 2-digit numbers without and with regrouping A8.8 Subtraction involving two 2-digit numbers without and with regrouping A8.9 Addition and subtraction using transforming, compensating, and other strategies A9.1 Higher decade addition and subtraction without and with bridging the decade A9.2 Partitioning and combining involving 2- digit numbers A9.3 Combining and partitioning involving subtraction; relate the non-canonical forms strategy to a written A9.4 Addition involving two 2-digit numbers method and explain the without and with regrouping reasoning used. A9.5 Subtraction involving two 2-digit numbers Understand that in adding without and with regrouping two-digit numbers, one IA8.1 Leap Frog adds tens and tens, ones IA8.2 Bead String with Ten Catcher and ones; and sometimes it IA8.3 Add or Subtract 11 is necessary to compose a IA8.4 Add to or Subtract from 49 ten. IA8.5 Calculator Challenge IA8.6 Jump to 100 IA8.7 Jump from 100 IA8.8 Target Number IA8.9 Walk-about Sequences IA8.10 Non-standard Measurement Plan IA9.1 Follow the Pattern IA9.2 Ten More or Ten Less IA9.3 Counting by Tens IA9.4 Add or Subtract Tens IA9.5 Adding Tens and Ones Using Money IA9.6 Screened Subtraction Tasks IA9.7 Split the Subtrahend (Multiples of 10) 5. Given a two-digit Given a two-digit number, mentally find 10 Tens/One Purple Book: F number, mentally find 10 more or 10 less than the number, without s 1 or 2 A8.1 Forward and backward number word more or 10 less than the having to count; explain the reasoning used. sequences by 10s, on and off the decade number, without having to A8.2 Adding from a decade and subtracting to count; explain the a decade reasoning used. A8.3 Adding to a decade and subtracting from © 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. a decade A8.4 Incrementing and decrementing by 10s on and off the decade A8.6 Adding 10s to a 2-digit number and subtracting 10s from a 2-digit number IA9.2 Ten More or Ten Less IA9.3 Counting by Tens IA9.4 Add or Subtract Tens IA9.5 Adding Tens and Ones Using Money IA9.6 Screened Subtraction Tasks IA9.7 Split the Subtrahend (Multiples of 10) 6. Subtract multiples of 10 Subtract multiples of 10 in the range 10-90 Tens/One Purple Book: F in the range 10-90 from from multiples of 10 in the range 10-90 s 1 or 2 A8.1 Forward and backward number word multiples of 10 in the range (positive or zero differences), using concrete sequences by 10s, on and off the decade 10-90 (positive or zero models or drawings and strategies based on A8.2 Adding from a decade and subtracting to differences), using concrete place value, properties of operations, and/or a decade models or drawings and the relationship between addition and A8.3 Adding to a decade and subtracting from strategies based on place subtraction; relate the strategy to a written a decade value, properties of method and explain the reasoning A8.4 Incrementing and decrementing by 10s operations, and/or the on and off the decade relationship between A8.6 Adding 10s to a 2-digit number and addition and subtraction; subtracting 10s from a 2-digit number relate the strategy to a IA9.2 Ten More or Ten Less written method and explain IA9.3 Counting by Tens the reasoning used. IA9.4 Add or Subtract Tens IA9.5 Adding Tens and Ones Using Money IA9.6 Screened Subtraction Tasks IA9.7 Split the Subtrahend (Multiples of 10) *F is Full; P is Partial; N is None

Measurement and Data 1.MD Measure lengths indirectly and by iterating length units. 1. Order three objects by length; compare the lengths of two objects indirectly by using a third object. 2. Express the length of an © 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps. *F is Full; P is Partial; N is None

Tell and write time. 3. Tell and write time in hours and half-hours using analog and digital clocks. *F is Full; P is Partial; N is None

Represent and interpret data. 4. Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. *F is Full; P is Partial; N is None

Geometry 1.G © 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. Reason with shapes and their attributes. 1. Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes. 2. Compose two- dimensional shapes (rectangles, squares, trapezoids, triangles, half- circles, and quarter-circles) or three dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.4 3. Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares. *F is Full; P is Partial; N is None

© 2011. Tina Silvestri & Will LaRiccia, Solon City Schools. 2See Glossary, Table 1. 3Students need not use formal terms for these properties. 4Students do not need to learn formal names such as “right rectangular prism.”