New York State Next Generation Mathematics Learning StandardsUnpacking Document (DRAFT)GRADE: KDOMAIN: Operations & Algebraic ThinkingCLUSTER: Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.Students build upon their understanding of counting to develop meanings for addition and subtraction by modeling how they put together or takeapart up to ten objects in different ways. As they encounter problem situations, they first use concrete objects, progress to drawing pictures, andthen translate these representations into equation form.Grade Level Standard:NY-K.OA.1 Represent addition and subtraction using objects, fingers, pennies, drawings, sounds, acting out situations, verbal explanations,expressions, equations, or other strategies.Note: Drawings need not show details but should show the mathematics in the problem.PERFORMANCE/KNOWLEDGE TARGETS(measurable and observable) Solve a given single digit addition or subtraction numeric problem that involves sums of tens using various manipulatives and strategies(i.e., dice, fingers, drawing, number lines, number grids, mental images, acting out, sounds (claps), verbal explanations).Describe addition in terms of “putting together”.Describe subtraction in terms of “taking away”.Create and explain a model that shows the solution to a given addition or subtraction numeric problem and translate that model intoequation form.ASPECTS OF 8.ConceptualApplicationMake sense of problems and persevere in solving them.Reason abstractly and quantitatively.Construct viable arguments and critique the reasoning of others.Model with mathematics.Use appropriate tools strategically.Attend to precision.Look for and make use of structure.Look for and express regularity in repeated reasoning.FOUNDATIONALUNDERSTANDING NY-PK.CC.3 Understand the relationship between numbers and quantities 10 10; connect counting to cardinality.NY-PK.OA.1 Explore addition and subtraction by using objects, fingers and responding to real world situations.NY-K.CC.3 Write number from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representinga count of no objects).NY-K.CC.5a Answer counting questions using as many as 20 objects arranged in a line, a rectangular array, and a circle.Answer counting questions using as many as 10 objects in a scattered configuration.
NYSED Draft Unpacking DocumentThe following pages contain EXAMPLES to support current instruction of the content standard and may be used at thediscretion of the teacher and adapted to best serve the needs of the learners in the classroom.Students begin to harness their practiced counting abilities, knowledge of the value of numbers, and work with embedded numbers toreason about and solve addition and subtraction expressions and equations.Concrete ObjectsDrawingsExample 1: Represent Decomposition and Composition Addition Stories to 8The following task is taken from EngageNY Grade K, Module 4, Lesson 15.Materials: (T) Cup containing 8 loose linking cubes or other smallmasking tape (S) Personal white boardmanipulatives,Stretch a line of tape or chalk down the middle of the rug, table, or desk.T:We are going to play the gravity game today! Let’s pretend my cubesare space rocks. Help me count how many rocks I am putting into mycup.S:1, 2, 3, 4, 5, 6, 7, 8.T:I have 8 space rocks in my cup. This side of the tape is the land(point), and this side is the ocean (point).I will use gravity and my magic tape line to help me find somenumber sentences about 8. How many space rocks fell on land, andhow many fell into the ocean? Let me shake it 8 times, and then, Iwill pour it out to see what happens! (Demonstrate and pour thecubes onto the surface.) What happened?S:There are some on that side of the line and some on this side. There are 6 on that side and 2 on this one!NOTES ONMULTIPLE MEANSOF ENGAGEMENT:Allow students with disabilities orstudents working below grade level,who might still need the scaffold, toengage in the lesson by continuing touse number bonds to show whathappened when the cubes werepoured out. Encourage them to writethe number sentences underneath.Page 2 of 5
NYSED Draft Unpacking DocumentThe following pages contain EXAMPLES to support current instruction of the content standard and may be used at thediscretion of the teacher and adapted to best serve the needs of the learners in the classroom.T:MP.4 S:Can we make a number sentence about our picture?We had 8 rocks, but they broke into a 2 and a 6. 8 2 6. 2 6 8.(Other varying responses.)T:Write the number sentence on your personal board.T:Did anyone think of a different number sentence that tells how our cubes look right now?(Allow time for sharing and discussion.)T:Let’s try it again and see if gravity can help us make another sentence! Student B, would you like to try? I wonder howmany different number sentences we can find about 8.Allow several more iterations of the game, directing students to represent the equations for the situation each time. List theequations on the board to help students appreciate all of their new names for 8. Ensure that students are confident as to theplacement of the addends and the total in their number sentences.Example 2: Represent Decomposition and Composition Addition Stories to 8The following task is taken from EngageNY Grade K, Module 4, Lesson 15.There are 8 shapes. Count and circle the squares. Count and circle the triangle. There are 8 flowers. Some flowers are yellow, and some flowers are red. Draw a picture to go with the story. Create your own story and tell your partner. Have your partner draw a picture of your story and create a number sentence to go withthe picture.Allowing students to generate their own stories provides opportunity for cultural responsiveness and the development ofmathematical language.Page 3 of 5
NYSED Draft Unpacking DocumentThe following pages contain EXAMPLES to support current instruction of the content standard and may be used at thediscretion of the teacher and adapted to best serve the needs of the learners in the classroom.Example 3: Multiple Representations of SubtractionThe following is taken from lesson 20, EngageNY K Module 4.Solve “take from with result unknown” expressions and equations using the minus sign with no unknown.Concrete objects and pictorial representations are tied to or matched to the representative subtraction expression or equation usingthe minus sign with no unknown. This progression helps students move from concrete processes to reasoning abstractly andquantitatively (MP.2).Materials:(S) 5 linking cubes, personal white boardT:Place your linking cubes on the table in front of you. Count them. How many do you have?S:There are 5.T:Put 3 linking cubes in your hand and take them away. How many are left on the table?S:2.T:Yes, 5 take away 3 is 2. There is a special Math Way to write what we just did. We had 5 cubes.I will write the number 5 to show all of the cubes together. (Demonstrate.) There is a special sign we can use when wewant to show that we are removing some cubes. It looks like this. (Write the minus sign.) How many did we take away?S:3.T:I write the 3 here. (Demonstrate.) You know the next part already!Our sign for is the same as or equals. (Write the equal sign.) Howmany were left on the table?S:2.T:I will write that here: 2. Read with me: 5 take away 3 equals 2.S:5 take away 3 equals 2.T:Let’s do another one. This time let’s make a picture on our boardsabout the cubes. Draw your 5 cubes. Now we want to take away 4.How should we show that we are taking them away?S:Cross them out.T:Cross out 4 cubes. How many cubes do you have left?S:1.T:Let’s write the number sentence together. I will write it on the classboard while you write it on your personal white board. 5 cubes take away 4 cubes is 1 cube. 5 – 4 1. Read it with me.NOTES ONMULTIPLE MEANSOF ACTION ANDEXPRESSION:Ask students working above grade level towrite their own take away math story andshow their solution in writing. Ask earlyfinishers to share their new stories witheach other and encourage them to solveas many stories as they come up with.Vary the use of the term equals bysometimes using is or is the same as.These multiple means of expression keepthe meaning of the symbol fresh.S:5 take away 4 is 1.T:Erase your board. I have a story for you! 5 students were playing on the slide. Draw a circle for each student on your board.2 of the students left to go to the swings. In your drawing, cross out the students who went to the swings. How manystudents were left at the slide?S:3.T:Help me write the number sentence, and write it on your board, too. How many students were thereat first?Page 4 of 5
NYSED Draft Unpacking DocumentThe following pages contain EXAMPLES to support current instruction of the content standard and may be used at thediscretion of the teacher and adapted to best serve the needs of the learners in the classroom.S:5.T:5 minus ? How many students went to the swings?S:2.T:5 – 2 equals ?S:3.T:Let’s read it all together: 5 – 2 3.S:5 – 2 3.T:On your board, draw pictures to make up a take away story of your own. Share your picture with your friend. Can you writethe number sentence that tells your story? (Allow time for writing and discussion.)T:Who would like to share their story and picture with the class?Example 4: Writing and Solving “Take From” EquationsThe following is taken from lesson 33, EngageNY Grade K, Module 4.Materials:(S) 9 teddy bears or other counters, 10 linking cubes, subtraction equation (Template), personal white boardT:(Write – .) Let’s pretend you have a family of 9 bears. Put 9 bears in front of you. One bear is hungry andwants to go to the honey tree! Take 1 bear and scoot him across your desk to show his adventure. 8 are left.T:Help me make a number bond about the story. (Allow students to offer guidance in creating the number bond on theboard.) Now we want to make a number sentence about this story. Are we adding more bears in this story or taking someaway?S:Taking away.T:Yes, we need to make a take away, or subtraction, number sentence.What number would we put in the first blank?S:How many we started with! 9.T:What goes in the next blank?S:The bear that went away. 1.T:What should we put in the blank after the equal sign?S:How many bears are still at home. 8.T:Great! Let’s write our number sentence. Fill in the blanks on your personal white board and read with me. (Demonstrate.)S:9 minus 1 is 8. 9 take away 1 leaves 8.T:Send your bear back home. Let’s pretend 2 bears are hungry thistime. Send them to the forest. We need to write a new numbersentence. What would we write this time? (Ask students to help fillin the blanks again, explaining why they chose each number.) Readthe number sentence with me.S:9 – 2 7.Continue with the activity several times, repeating the pattern through 9 – 8and having students write and read the equation each time.NOTES ONMULTIPLE MEANSOF REPRESENTATION:Introduce unfamiliar words to English languagelearners by holding up a counting bear whilesaying a family of bears and showing pictures fortree and forest. This allows them to focus on themath and expand their vocabulary, which in turnhelps them explain their thinking during partnershares.Example 5: Use nursery rhymes and songs to have students model additionand subtractions scenarios. For example, subtraction can be modeled by the lyrics in “Five Little Monkeys Jumping on the Bed”.Page 5 of 5