Common Core State Standards 2nd Edition Math Pacing Guide Kindergarten—3RD Nine Week Period 2nd Edition Developed by: Christy Mitchell, Elizabeth Johnson, Michelle Estrada ````````````````````````````````````````````````````````````````````````````````````````````````````````````` Mr. Stan Rounds, Superintendent Dr. Steven Sanchez, Associate Superintendent for Learning, Teaching & Research Prepared By: Lydia Polanco, Coordinator of Elementary Instruction st
1 Edition Developed by: Elizabeth Johnson, Deborah Paul, Deborah Romero 1 Understanding Mathematics: The standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it.1 Mathematical understanding and procedural skill are equally important.2 Description of the Pacing Guide: A pacing guide is an interval based description of what teachers teach in a particular grade or course; the order in which it is taught, and the amount of time dedicated to teaching the content. Purpose of a Pacing Guide: The purpose of a pacing guide is to ensure that all of the standards are addressed during the academic year. Each pacing guide is nine weeks in duration. Components of the Pacing Guide: •
Critical Areas-­‐ Each grade level has identified Critical Areas. These areas are woven throughout the standards and should receive additional time and attention. •
Mathematical Practice Standards (8)-­‐ Based on the NCTM Process Standards, these standards describe the variety of "processes and proficiencies" students should master while working with the Grade Level Content Standards. •
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Domains are larger groups of related Content Standards. Standards from different domains may sometimes be closely related.3 Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.4 Grade level standards define what students should know and be able to do by the end of each grade level. Unpacked standards provide a clear picture for the teacher as he/she implements the CCSS Depth of Knowledge — (DOK) Criteria for systematically analyzing the alignment between standards and standardized assessments •
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www.corestandards.org, Mathematics, Introduction, p. 4 See #1 3
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www.corestandards.org, Mathematics, Introduction, p. 5 2
2 STANDARDS-­‐BASED, STANDARDS-­‐DRIVEN Other Resources LCPS Pacing Guides Common Core State Standards Core Program enVision Math Supplemental Technology Based program to prepare for PARCC (First in Math, FASTT Math, etc.) 3 Grade Level: Kindergarten Quarter: 3rd 9 weeks Domain: Counting and Cardinality Critical Areas: #1 Strong Connection Grade Level Content Standard K.CC.1 Count to 100 by ones and by tens (3rd quarter to 50) K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). (3rd quarter to 50) Standard Q1 Q2 Q3 K.CC.1 I/P I/P I/P K.CC.2 I/P I/P R Cluster: Know number names and the count sequence #2 #3 #4 Q4 P P Mathematical Practice Standards MP.6 Attend to precision ●Express numerical answers with a degree of precision appropriate for the problem context. MP.7 Look for and make use of structure ●Look for the overall structure and patterns in mathematics. Unpacked Content Standard: K.CC.1 calls for students to rote count by starting at one and count to 100. When students count by tens they are only expected to master counting on the decade (0, 10, 20, 30, 40 …). This objective does not require recognition of numerals. It is focused on the rote number sequence. The emphasis of this standard is on the counting sequence to 100. K.CC.2 includes numbers 0 to 100. This asks for students to begin a rote forward counting sequence from a number other than 1. Thus, given the number 14, the student would count, “14, 15, 16 …” This objective does not require recognition of numerals. It is focused on the rote number sequence. Vocabulary: count, number, tens, ones, zero , order, forward, represent, set Resources: Depth of Knowledge enVision Math K.CC.1 DOK 1: Recite numbers as stated in standard Topics 1-­‐6 Interactive Digital Path Topics 1-­‐6 K.CC.2 DOK 1: Can you identify the number that comes after 7? Daily Routine K.CC.1 Students count aloud while clapping, slapping, etc. Count objects in estimating jar. Count while pointing to a number line K.CC.2 Count forward, starting from a different number daily. Given a story problem students count on to determine the answer 4 Grade Level: Kindergarten Quarter: 3rd 9 weeks Domain: Counting and Cardinality Critical Areas: #1 Strong Connection Standard Q1 Q2 X I K.CC.5 K.CC.6 X I K.CC.7 X I Cluster: Count to Tell the Number of Objects #2 #3 #4 Q3 P P P Q4 R R R Grade Level Content Standard Mathematical Practice Standards K.CC.5 Count to answer ―how many?‖ questions about as many MP.6 Attend to precision as 20 things arranged in a line, a rectangular array, or a circle, or ●Express numerical answers with a degree of precision appropriate for the problem context. as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. MP.7 Look for and make use of structure K.CC.6 Identify whether the number of objects in one group is ●Look for the overall structure and patterns in mathematics. greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. K.CC.7 Compare two numbers between 1 and 10 presented as written numerals. Unpacked Content Standard: K.CC.5 addresses various counting strategies. Based on early childhood mathematics experts, such as Kathy Richardson, students go through a progression of four general ways to count. These counting strategies progress from least difficult to most difficult. • First, students move objects and count them as they move them. • The second strategy is that students line up the objects and count them. Third, students have a scattered arrangement and they touch each object as they count. • Lastly, students have a scattered arrangement and count them by visually scanning without touching them. Since the scattered arrangements are the most challenging for students, K.CC.5 calls for students to only count 10 objects in a scattered arrangement, and count up to 20 objects in a line, rectangular array, or circle. Out of these 3 representations, a line is the easiest type of arrangement to count. K.CC.6 Expects mastery of up to ten objects. Students can use matching strategies (Student 1), counting strategies or equal shares (Student 3) to determine whether one group is greater than, less than, or equal to the number of objects in another group. Student 1 Student 2 Student 3 5 Lined up one square and one triangle. Since there is one extra triangle, there are more triangles than squares. Δ ΔΔΔΔΔΔ Counted the squares and I got 8. Then I counted the triangles and got 9. Since 9 is bigger than 8, there are more triangles than squares. Put them in a pile. I then took away objects. Every time I took a square, I also took a triangle. When I had taken almost all of the shapes away, there was still a triangle left. That means that there are more triangles than squares. K.CC.7 Calls for students to apply their understanding of numerals 1-­‐10 to compare one from another. Thus, looking at the numerals 8 and 10, a student must be able to recognize that the numeral 10 represents a larger amount than the numeral 8. Students should begin this standard by having ample experiences with sets of objects (K.CC.3 and K.CC.6) before completing this standard with just numerals. Based on early childhood research, students should not be expected to be comfortable with this skill until the end of Kindergarten. Vocabulary: order, count, zero, number, add, set, group, line, array, circle, scattered, greater than, /more/most, less than/less/least, equal to , matching, take away Resources: Depth of Knowledge enVision Math K.CC.5 DOK 1: Students recite and repeat the same number of Topics 1-­‐6 objects for varying objects. Interactive Digital path Topics 1-­‐6 K.CC.5 DOK 2: Students construct different arrangements with a larger number of objects. Ex: show me twenty on a ten frame in a rectangle etc. K.CC.5 DOK 3: Students compare and explain different arrangements with a larger number of objects. K.CC.6 DOK 2: How would you compare these 2 groups by using matching and counting strategies? K.CC.6 DOK 3: Can you construct a group that is one less, one more, and equal to a given set of objects? (i.e. task cards and recording sheet) K.CC.7 DOK 2: Students compare two written numerals using manipulatives. K.CC.7 DOK 3: Students develop a logical argument and explanation. Can you use a math tool (i.e. 100’s chart, 10 frame, number line, or unifix cubes) to show the comparison of 2 numbers? How can you show me that 10 is greater than 4? 6 Grade Level: Kindergarten Quarter: 3rd 9 weeks Standard Q1 Q2 Q3 Q4 K.OA.1 I I I P K.OA.2 I I I P K.OA.3 X I I P K.OA.4 X X I P K.OA.5 X X I P Domain: Operations and Algebraic Thinking Cluster: Understand addition is putting together and adding to understand subtraction as taking apart and taking from Critical Areas: #1 Strong Connection #2 #3 #4 Grade Level Content Standard Mathematical Practice Standards K.OA.1 Represent addition and subtraction with objects, MP.6 Attend to precision fingers, mental images, drawings, sounds (e.g., claps), acting ●Express numerical answers with a degree of precision out situations, verbal explanations, expressions, or equations. appropriate for the problem context. (Drawings need not show details, but should show the mathematics in the problems. This applies wherever drawings MP.7 Look for and make use of structure are mentioned in the Standards.) ●Look for the overall structure and patterns in mathematics K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawing to represent the problem. (3rd Quarter – addition only) K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). (3rd Quarter – thru 5) K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. K.OA.5 Fluently add and subtract within 5. (2nd quarter: Introduces Addition, 3rd quarter: Introduces subtraction, and become proficient in addition, 4th quarter proficient in subtraction) Unpacked Content Standard: 7 K.OA.1 asks students to demonstrate the understanding of how objects can be joined (addition) and separated (subtraction) by representing addition and subtraction situations in various ways. (Using objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.) This objective is primarily focused on understanding the concept of addition and subtraction rather than merely reading and solving addition and subtraction number sentences (equations). K.OA.2 Kindergarteners use counting to solve the four problem types by acting out the situation and/or with objects, fingers, and
drawings. Kindergarten students solve four types of problems within 10:
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Result Unknown/Add To
Result Unknown/Take From
Total Unknown/Put Together-Take Apart
Addend Unknown/Put Together-Take Apart Add To Take From Put Together/Take Apart Put Together/Take Result Unknown Result Unknown Total Unknown Apart Addend Unknown Two bunnies sat on the grass. Five apples were on the table. I Three red apples and Five apples are on the table. Three more bunnies hopped ate two apples. two green apples are on the Three are red and the rest are there. How many apples are on the table. How many apples are on green. How many apples are How many bunnies are on the table now? the table? green? grass now? 5 – 2 = ? 3 + 2 = ? 3 + ? = 5, 5 – 3 = ? 2 + 3 = ? K.OA.3 asks students to understand that a set of (5) object can be broken into two sets (3 and 2) and still be the same total amount (5). The focus is on number pairs which add to a specified total 1-­‐10. In addition, this standard asks students to understand that a set of objects (5) can be broken in multiple ways (3 and 2; 4 and 1). Thus, when breaking apart a set (decomposing), students develop the understanding that a smaller set of objects exists within that larger set (inclusion). This should be developed in context before moving into how to represent decomposition with symbols (+, -­‐, =). Example: ―Bobby Bear is missing 5 buttons on his jacket. How many ways can you use blue and red buttons to finish his jacket? Draw a picture of all your ideas. Students could draw pictures of: 4 blue and 1 red button 3 blue and 2 red buttons 2 blue and 3 red buttons 1 blue and 4 red buttons After the students have had numerous experiences with decomposing sets of objects and recording with pictures and numbers, the teacher eventually makes connections between the drawings and symbols: 5=4+1, 5=3+2, 5=2+3, and 5=1+4 The number sentence 8 only comes after pictures or work with manipulatives, and students should never give the number sentence without a mathematical representation. K.OA.4 builds upon the understanding that a number can be decomposed into parts (K.OA.3).The number pairs that total ten are foundational for students’ ability to work fluently within numbers and operations. Different models, such as ten-­‐frames, cubes, two-­‐color counters, etc., assist students in visualizing these number pairs for ten. Once students have had experiences breaking apart ten into various combinations, this asks students to find a missing part of 10. Examples:
When working with shapes of 2 different colors, a student determines that 4 more shapes are needed to make a total of 10.
I have 6 shapes. I need 4 more shapes to have 10 in all.
A full case of juice boxes has 10 boxes. There are only 6 boxes in this case. How many juice boxes are missing?
Student 1 Student 2 Student 3 Using a Ten Frame I used 6 counters for Think Addition I counted out 10 cubes Basic Fact I know that it’s 4 because the 6 boxes of juice still in the case. There because I knew there needed to be ten. I 6 and 4 is the same amount as 10. are 4 blank spaces so 4 boxes have been pushed these 6 over here because they removed. This makes sense since 6 and 4 were in the container. These are left over. more equal 10. So there’s 4 missing. •
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Strategies students may use to attain fluency include: Counting on (e.g., for 3+2, students will state, ―3, and then count on two more, ―4, 5, and state the solution is ―5) Counting back (e.g., for 4-­‐3, students will state, ―4, and then count back three, ―3, 2, 1 and state the solution is ―1) Counting up to subtract (e.g., for 5-­‐3, students will say, ―3, and then count up until they get to 5, keeping track of how many they counted up, o Stating that the solution is ―2) Using doubles (e.g., for 2+3, students may say, ―I know that 2+2 is 4, and 1 more is 5) Using commutative property (e.g., students may say, ―I know that 2+1=3, so 1+2=3) Using fact families (e.g., students may say, ―I know that 2+3=5, so 5-­‐3=2) 9 K.OA.5 is introduced in the third nine weeks. It uses the word fluently, which means accuracy (correct answer), efficiency (a reasonable amount of steps), and flexibility (using strategies such as the distributive property). Fluency is developed by working with many different kinds of objects over an extended amount of time. Traditional flash cards or timed tests have not been proven as effective instructional strategies for developing fluency. Vocabulary: count, number, tens, ones, zero , order, forward, represent, set Resources: Depth of Knowledge enVision Math K.OA.1 DOK 2: Show me how to add or subtract? Topics 7-­‐9 K.OA.2 DOK 3: Students construct their own equation and Interactive Digital Path Topic 7-­‐9 record their thinking. K.O.A.3 DOK 3: Students construct, compare, develop logical Daily Routine: arguments and formulation within the components of this Using the date or a story problem have students solve addition standard. problems using objects or mental images. Make sure to record K.O.A.4 DOK 2: Students use manipulatives to show the missing equation to show students’ thinking. addend. K.O.A.4 DOK 3: Students solve equations with the missing addend without manipulatives . Ex: 4 + ☐ = 9. Students develop a logical argument -­‐ Can you show how you figured this out? K.O.A.5 DOK 1: Student recall of facts. 10 Grade Level: Kindergarten Quarter: 3rd 9 weeks Domain: Number and Operation Base Ten Standard Q1 Q2 Q3 Q4 K.NBT.1 I I I P Cluster: Work with numbers 11-­‐19 to gain foundations for place value Critical Areas: #1 Strong Connection #2 #3 #4 Grade Level Content Standard Mathematical Practice Standards K.NBT 1. Compose and decompose numbers from 11-­‐ 19 into MP.6 Attend to precision ten ones and some further ones, (e.g., by using objects or ●Communicate precisely with others and try to use clear drawing) and record each composition or decomposition by a mathematical language when discussing their reasoning. drawing or equation (e.g., 18=10+8); understand that these numbers are composed of ten ones and one, two, three, four, MP.7 Look for and make use of structure five, six, seven, eight, or nine ones. ●Look for the overall structure and patterns in mathematics Unpacked Content Standard: K.NBT 1 Students explore numbers 11-­‐19 using representations, such as manipulatives or drawings. Keeping each count as a single unit, kindergarteners use 10 objects to represent “10” rather than creating a unit called a ten (unitizing) as indicated in the First Grade CCSS standard 1.NBT.1a: 10 can be thought of as a bundle of ten ones — called a “ten.” •
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Example: Teacher: “I have some chips here. Do you think they will fit on our ten frame? Why? Why Not?” Students: Share thoughts with one another. Teacher: “Use your ten frame to investigate.” Students: “Look. There’s too many to fit on the ten frame. Only ten chips will fit on it.” Teacher: “So you have some leftovers?” Students: “Yes. I’ll put them over here next to the ten frame.” Teacher: “So, how many do you have in all?” Student A: “One, two, three, four, five… ten, eleven, twelve, thirteen, fourteen. I have fourteen. Ten fit on and four didn’t.” Student B: Pointing to the ten frame, “See them-­‐ that’s 10… 11, 12, 13, 14. There’s fourteen.” Teacher: Use your recording sheet (or number sentence cards) to show what you found out. •
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Eleven and twelve are special number words.
Teen means one ―ten plus ones.
The verbal counting sequence for teen numbers is backwards – we say the ones digit before the tens digit.
For example ―27 reads tens to ones (twenty-seven), but 17 reads ones to tens (seven-teen).
In order for students to interpret the meaning of written teen numbers, they should read the number as well as describe the quantity.
For example, for 15, the students should read ―fifteen and state that it is one group of ten and five ones and record that 15 = 10 + 5.
Special attention needs to be paid to this set of numbers as they do not follow a consistent pattern in the verbal counting sequence.
Common Misconceptions:
11 Students have difficulty with ten as a singular word that means 10 things. For many students, the understanding that a group of 10
things can be replaced by a single object and they both represent 10 is confusing. Help students develop the sense of ten by first
using group able materials then replacing the group with an object or representing 10, such as a rod or 10 Frame. Watch for and
address the issue of attaching words to materials and groups without knowing what they represent. If this misconception is not
addressed early on it can cause additional issues when working with numbers 11-19 and beyond. Vocabulary: fluency, add, subtract Resources: enVision Math Topics 10-­‐11 Interactive Digital Path Topic 10-­‐11 Depth of Knowledge K.NBT.1 DOK 2: Students are showing objects or drawings of a number between 11-­‐19 and recording their findings 12 Grade Level: Kindergarten Quarter: 3rd 9 weeks Standard Q1 Q2 Q3 Q4 K.MD.1 X I I P K.MD.2 X I I P Domain: Measurement and Data Cluster: Describe and compare measurable attributes Critical Areas: #1 #2 Strong #3 #4 Connection Grade Level Content Standard Mathematical Practice Standards K.MD 1. Describe measureable attributes of objects, such as MP.6 Attend to precision length or weight. Describe several measureable attributes of a ●Communicate precisely with others and try to use clear single object. mathematical language when discussing their reasoning. K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less MP.7 Look for and make use of structure ●Look for the overall structure and patterns in mathematics. of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Unpacked Content Standard: K.MD.1 calls for students to describe measurable attributes of objects, such as length and weight. In order to describe attributes such as length and weight, students must have many opportunities to informally explore these attributes. Students should state comparisons of objects verbally and then focus on specific attributes when making verbal comparisons for K.MD.2. They may identify measurable attributes such as length, width, height, and weight. Example: •
When describing a soda can, a student may talk about how tall, how wide, how heavy, or how much liquid can fit inside. These are all measurable attributes. Non-­‐measurable attributes include: words on the object, colors, pictures, etc. This standard focuses on using descriptive words and does not mean that students should sort objects based on attributes. (Sorting appears later) K.MD.2 asks for direct comparisons of objects. Direct comparisons are made when objects are put next to each other, such as two children, two books, two pencils. For example, a student may line up two blocks and say, “This block is a lot longer than this one.” Students are not comparing objects that cannot be moved and lined up next to each other. Through ample experiences with comparing different objects, children should recognize that objects should be matched up at the end of objects to get accurate measurements. Since this understanding requires conservation of length, a developmental milestone for young children, children need multiple experiences to move beyond the idea that …. “Sometimes this block is longer than this one and sometimes it’s shorter (depending on how I lay them side by side) and that’s okay.” “This block is always longer than this block (with each end lined up appropriately).” Before conservation of length: The striped block is longer than the plain block when they are lined up like this. 13 But when I move the blocks around, sometimes the plain block is longer than the striped block. After conservation of length: I have to line up the blocks to measure them. The plain block is always longer than the striped block. Vocabulary: length, weight, size, attribute Resources: Depth of Knowledge enVision Math K. MD.1 DOK 1: Students measure objects using Topics 12-­‐13 nonstandard/standard forms of measurement to describe Interactive Digital Path Topics 12-­‐13 length, width, height, and weight. K.MD.1 DOK 2: Students make a prediction before measuring objects using nonstandard/standard forms of measurement to describe length, width, height, and weight. K.MD.2 DOK 2: Students compare measurement of two objects using nonstandard/standard forms of measurement to describe length, width, height, and weight. K.MD.2 DOK 3: Students compare measurement of three or more objects using nonstandard/standard forms of measurement to describe length, width, height, and weight and record findings. 14 Grade Level: Kindergarten Quarter: 3rd 9 weeks Domain: Measurement and Data Standard Q1 Q2 Q3 Q4 K.MD.3 I I P R Cluster: Classify objects and count the number of objects in each category Critical Areas: #1 #2 Strong #3 #4 Connection Grade Level Content Standard Mathematical Practice Standards K.MD.3 Classify objects into given categories; count the MP.6 Attend to precision numbers of objects in each category and sort the categories by ●Communicate precisely with others and try to use clear count. (Limit category counts to be less than or equal to 10) mathematical language when discussing their reasoning. MP.7 Look for and make use of structure ●Look for the overall structure and patterns in mathematics. Unpacked Content Standard: K.MD.3 is introduced in the third nine weeks. It tasks students to identify similarities and differences between objects (e.g., size, color, shape) and use the identified attributes to sort a collection of objects. Once the objects are sorted, the student counts the amount in each set. Once each set is counted, then the student is asked to sort (or group) each of the sets by the amount in each set. For example, when given a collection of buttons, the student separates the buttons into different piles based on color (all the blue buttons are in one pile, all the orange buttons are in a different pile, etc.). Then the student counts the number of buttons in each pile: blue (5), green (4), orange (3), purple (4). Finally, the student organizes the groups by the quantity in each group (Orange buttons (3), Green buttons next (4), Purple buttons with the green buttons because purple also had (4), Blue buttons last (5). This objective helps to build a foundation for data collection in future grades. In later grade, students will transfer these skills to creating and analyzing various graphical representations. Vocabulary: sort, same, different, size, color, shape, attributes, Resources: Depth of Knowledge enVision Math K.MD.3 DOK 2: Students classify and compare objects based on Topics 12-­‐13 common attributes. Interactive Digital Path Topics 12-­‐13 K.MD.3 DOK 3: Students create chart, graphic organizer or Venn Diagram to show data. 15 Grade Level: Kindergarten Quarter: 3rd 9 weeks Domain: Geometry Critical Areas: #1 Standard Q1 Q2 Q3 Q4 K.G.1 I/P R I/P R K.G.2 I/P R I/P R K.G.3 X X I/P R Cluster: Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). #2 Strong #3 #4 Connection Mathematical Practice Standards MP.6 Attend to precision ● Communicate precisely with others and try to use clear mathematical language when discussing their reasoning. MP.7 Look for and make use of structure ● Look for the overall structure and patterns in mathematics. Grade Level Content Standard K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. (3rd Quarter – hexagons, cubes, cones, cylinders, and spheres). K.G.2 Correctly name shapes regardless of their orientations or overall size. (3rd Quarter -­‐ see shapes listed above) K.G.3 Identify shapes as two-­‐dimensional (lying in a plane, “flat”) or three dimensional (“solid”). Unpacked Content Standard: KG.1 is introduced and has to be proficient and it expects students to use positional words (such as those italicized above) to describe objects in the environment. Kindergarten students need to focus first on location and position of two-­‐and-­‐three-­‐
dimensional objects in their classroom prior to describing location and position of two-­‐and-­‐three-­‐dimension representations on paper. K.G.2 addresses students’ identification of shapes based on known examples. Students at this level do not yet recognize triangles that are turned upside down as triangles, since they don’t “look like” triangles. Students need ample experiences looking at and manipulating shapes with various typical and atypical orientations. Through these experiences, students will begin to move beyond what a shape “looks like” to identifying particular geometric attributes that define a shape. K.G.3 asks students to identify flat objects (2 dimensional) and solid objects (3 dimensional). This standard can be done by having students sort flat and solid objects, or by having students describe the appearance or thickness of shapes. Vocabulary: circle, square, triangle, rectangle, hexagon, cube, cone, cylinder, sphere Resources: Depth of Knowledge enVision Math K.G.1 DOK 1: Students recognize and recall shapes and Topics 14-­‐16 positions. Interactive Digital Path Topics 14-­‐16 K.G.1 DOK 2: Students create a shape book or poster relating 16 shapes to “real life” objects. K.G.2 DOK 1: Students recognize and name shapes. K.G.2 DOK 2: Students classify “real life” objects and label with shapes names. 17 Grade Level: Kindergarten Quarter: 3rd 9 weeks Domain: Geometry Critical Areas: #1 Standard Q1 Q2 Q3 Q4 K.G.4 I/P R I/P R K.G.5 I/P R I/P R K.G.6 X I P R Cluster: Analyze, compare, create and compose shapes #2 Strong #3 #4 Connection Mathematical Practice Standards MP.6 Attend to precision ●Communicate precisely with others and try to use clear mathematical language when discussing their reasoning. MP.7 Look for and make use of structure ●Look for the overall structure and patterns in mathematics. Grade Level Content Standard K.G.4 Analyze and compare two-­‐ and three-­‐dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length). (3rd Quarter – hexagons, cubes, cones, cylinders, and spheres) K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. K.G.6 Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides touching to make a rectangle?” Unpacked Content Standard: K.G.4 has to be introduced and be proficient during the third nine weeks. During the 1st nine weeks covers two-­‐dimensional shapes: (square, circle, triangle, and rectangle), 3rd nine weeks three-­‐dimensional shapes (hexagon, cube, cone, cylinder, and sphere). Students are asked to note similarities and differences between and among 2-­‐D and 3-­‐D shapes using informal language. These experiences help young students begin to understand how 3-­‐dimensional shapes are composed of 2-­‐dimensional shapes (e.g.., The base and the top of a cylinder is a circle; a circle is formed when tracing a sphere). K.G.5 asks students to apply their understanding of geometric attributes of shapes in order to create given shapes. For example, a student may roll a clump of play-­‐doh into a sphere or use their finger to draw a triangle in the sand table, recalling various attributes in order to create that particular shape. 3rd nine weeks three-­‐dimensional shapes (see K.G.4) K.G.6 has to be introduced in the third nine weeks. It moves beyond identifying and classifying simple shapes to manipulating two or more shapes to create a new shape. This concept begins to develop as students’ first move, rotate, flip, and arrange puzzle pieces. Next, students use their experiences with puzzles to move given shapes to make a design (e.g., “Use the 7 tan gram pieces to make a fox.”). Finally, using these previous foundational experiences, students manipulate simple shapes to make a new shape. Vocabulary: same, different, flat, solid, shape, side, length, circle, triangle, square, rectangle, sphere, cylinder, cube, cone, 18 hexagon, angle, equal Resources: enVision Math Topics 14-­‐16 Interactive Digital Path Topics 14-­‐16 Depth of Knowledge K.G.4 DOK 2: Student analyzes and compares 2D and 3D (sides, faces, and corners). K.G.4. DOK 3: Student constructs a Venn Diagram or T-­‐chart sorting shapes according to attributes. K.G.5 DOK 2: Student constructs shapes like pattern block puzzles K.G.5 DOK 3: Student constructs and compares shapes (ex: showing more than 1 way to make a shape). K.G.6 DOK 2: Student constructs shapes (ex. pattern block puzzles). K.G.6 DOK 3: Student constructs and compares shapes (ex. Showing more than 1 way to make the shape. 19 Daily Math Routines Suggestions for Kindergarten *Establishing daily math routines is an essential component of building, and reviewing, foundational skills in Kindergarten to ensure mastery of Common Core State Standards. enVisionMATH does not have a daily routine component; however, these are some suggestions to include in your daily routine. This is just a suggested list of activities to choose from daily as best fits into your schedule. Counting and Cardinality: • Counting to the date • Skip Counting (2’s, 5’s, and 10’s) • Counting objects in estimating jar • Counting number of student present/absent • Counting hot/cold lunches • Counting number of days in school • Counting on from a given number Operations and Algebraic Thinking • Create an equation of the day that equals the date Number and Operations in Base Ten • Bundling the straws, adding sticks, etc… to equal the number of days we’ve been in school. Measurement and Data • Comparing heights of children • Sorting attributes using kids (i.e. stripes/no stripes, tennis shoes/sandals) • Weather chart/graph Geometry • Engaging ways of demonstrating relative position using kids, interactive white board, drawing on white board, etc… • Shape of a day/Shape of the week (introduce/review) o Using math vocabulary (i.e. faces, sides, corners, 2-­‐D/3-­‐D, real-­‐life shape connections) 20 21