GarveySchool District
2014-15 Kindergarten Mathematics Curricular Guide
Shifting to greater focus and better coherence to achieve greater depthwith dual intensity
A Relentless Focus on…
- Whole Numbers
- Operations of Those Whole Numbers
- K-2: addition and subtraction
- The Quantities Those Whole Numbers Measure
Coherence ….
- Building new learning on what was previously learned
- A constant effort to rethink all the math we’re learning so that it links tightly into the core masteries that matter most. How are whole numbers, addition, and shapes related?
Depth…
- Fluency: Speed and accuracy with operations, developing memory and automaticity.
- K: add and subtract within five
- Deep Understanding: Ability to use math even in situations you haven’t been directly trained in and in more complex situations.
- Application: The capacity to know how to apply mathematical knowledge to situations even when not prompted to do so.
Dual Intensity . . .
The intensity of fluency and the intensity of application and understanding
Both procedural practice and a deep understanding of the meaning of what we’re doing and knowing how and when to apply it is essential to becoming proficient and experts in mathematics. Both must be practice with equal intensity just like a musician must practice both repetitive scales and simple and complex musical pieces to improve in their craft.
--Coleman, David. “Focus in the CommonCoreState Standards”
Shifts In MathematicsShift / Category / Description
Shift 1 / Focus / Teachers significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards.
Shift 2 / Coherence / Principals and teachers carefully connect the learning within and across grades so that students can build new understanding onto foundations built in previous years.
Shift 3 / Fluency / Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions.
Shift 4 / Deep
Understanding / Students deeply understand and can operate easily within a math concept before moving on. They learn more than the trick to get the answer right. They learn the math.
Shift 5 / Application / Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so.
Shift 6 / Dual Intensity / Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity.
Standards for Mathematical Practice
OVERARCHING HABITS OF MINDOF A
PRODUCTIVE MATHEMATICAL THINKER / 1. Make sense of problems and persevere in solving them.
6. Attend to precision. / REASONING AND EXPLAINING
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
MODELING AND USING TOOLS
4. Model with mathematics.
5. Use appropriate tools strategically.
SEEING STRUCTURE AND GENERALIZING
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Grade K Overview
Counting and Cardinality
Know number names and the count sequence.
Count to tell the number of objects.
Compare numbers.
Operations and Algebraic Thinking
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
Number and Operations in Base Ten
Work with numbers 11–19 to gain foundations for place value.
Measurement and Data
Describe and compare measurable attributes.
Classify objects and count the number of objects in categories.
Geometry
Identify and describe shapes.
Analyze, compare, create, and compose shapes.
Grade K
Counting and Cardinality K.CC(FOCUS)
Know number names and the count sequence.
K.CC.1. Count to 100 by ones and by tens.
K.CC.2.Count forward beginning from a given number within the known sequence
(instead of having to begin at 1).
K.CC.3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
Count to tell the number of objects. (0-20)
K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality.
K.CC.4.a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.
K.CC.4.b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.
K.CC.4.c. Understand that each successive number name refers to a quantity that is one larger.
K.CC.5. Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects.
Compare numbers.(0-10)
K.CC.6. Identify whether the number of objects in one group is 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.
Operations and Algebraic Thinking K.OA(FOCUS)
Understand addition as putting together and adding to, and understand subtraction as taking apart
and taking from.(within 10)
K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
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).
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 record the answer with a drawing or equation.
K.OA.5.Fluently add and subtract within 5.
1Include groups with up to ten objects.
2Drawings need not show details, but should show the mathematics in the problem.
(This applies wherever drawings are mentioned in the Standards.)
Number and Operations in Base Ten K.NBT(SUPPORTING)
Work with numbers 11–19 to gain foundations for place value.
K.NBT.1. Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18= 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.
Measurement and Data K.MD(SUPPORTING)
Describe and compare measurable attributes.
K.MD.1. Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.
K.MD.2. Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of” the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.
Classify objects and count the number of objects in each category.
K.MD.3. Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.3
Geometry K.G(SUPPORTING)
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones,
cylinders, and spheres).
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.
K.G.2. Correctly name shapes regardless of their orientations or overall size.
K.G.3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).
Analyze, compare, create, and compose shapes.
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).
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?”
3Limit category counts to be less than or equal to 10.
Instructional Period 1The Overall Focus is for Students to Count to 100 by Ones, Represent, Use Objects, and Write Numbers to 20
Big Idea/
Topic / Essential Standards / Knowledge/Skills/Process / Academic Vocabulary
Content Vocabulary / Instructional Materials and Days
Counting and Cardinality
Know number names and the count sequence.
Numbers to 20 / K.CC.1Count to 100 by ones and by tens. / 1.1Count to 100 by ones. / Sequence
Write
Represent
T 1:
Numbers 1-5
Count
number / Topic 1
Numbers 1-5
K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality. / 4.0 – 5.0 Count objects
K.CC.4.a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. / 4.a. Count each object in order with correct number name.
K.CC.4.b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. / 4.b.1.Understand that the last number name said tells how many objects altogether.
4.b.2. Understand that the rearrangement of objects does not change the total number of objects.
4.b.3 Understand that the number of objects does not change regardless of which object gets counted first.
K.CC.5. Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1–20, count out that many objects. / 5.1 Count to answer “how many?” up to 20 objects in:
- A line
- A rectangular array
- A circle
Counting and Cardinality
Count to tell the number of objects. / K.CC.3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). / 3.1. Write numbers from 0 to 20.
3.2 Represent a number of objects from 0 to 20. / Object
T 2:
More (than), fewer (than), Order, Same number of,
Same as, First,
Second, Third, Fourth, fifth, Column, Row, Zero, As Many, Fewest, Most, / Topic 2
More and Fewer
K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality. / 4.0 – 5.0 Count objects
c. Understand that each successive number name refers to a quantity that is one larger.
Comparing Numbers / K.CC.6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1 / 6.1 Identify the number of objects that are greater than or equal.
6.2 Identify the number of objects that are greater than or equal.
Know number names and the count sequence. / K.CC.3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). / 3.1. Write numbers from 0 to 20.
3.2 Represent a number of objects from 0 to 20. / T 3:
Numbers 6-10, Growing Pattern / Topic 3
Numbers 6-10
Count to tell the number of objects. / K.CC.4.b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. / 4.b.1. Understand that the last number name said tells how many objects altogether.
4.b.2. Understand that the rearrangement of objects does not change the total number of objects.
4.b.3 Understand that the number of objects does not change regardless of which object gets counted first.
Counting and Cardinality Know number names and the count sequence. / K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). / 2.0 Count forward from a given number. / Identify
Compare
T 4:
Greater, less, Forward, Backward, Order, Number Line / Topic 4
Comparing Numbers 0-10
Comparing Numbers / K.CC.6. Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies.1 / 6.1 Identify the number of objects that are greater than or equal.
6.2 Identify the number of objects that are greater than or equal.
K.CC.7. Compare two numbers between 1 and 10 presented as written numerals. / 7.0 Compare numbers.
Know number names and the count sequence. / K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). / 2.0 Count forward from a given number. / Write
Represent
T 5:
Numbers 11-20
Identify
Compose
Decompose
Objects, greater than, equal, numbers 11 to 19 / Topic 5
Numbers to 20
Count to tell the number of objects. / K.CC.4.b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. / 4.b.1. Understand that the last number name said tells how many objects altogether.
4.b.2. Understand that the rearrangement of objects does not change the total number of objects.
4.b.3 Understand that the number of objects does not change regardless of which object gets counted first.
Review Numbers 0-20
and/or
Frontload or Begin Teaching Numbers to 100 / Review Topics 1-5
and/orFrontload or Begin Teaching Topic 6
Numbers to 100 will Not Be Assessed in B1
Only numbers to 20
Benchmark
1
Instructional Period 2
The Focus is to
Count to 100 by tens, Count, Represent, Use Objects, and Write Numbers to 20
Add and Solve Word Problems within 10 and AddFluently Within 5
Big Idea/
Topic / Essential Standards / Knowledge/Skills/Process / Academic Vocabulary
Content Vocabulary / Instructional Materials and Days
Counting and Cardinality
Know number names and the count sequence.
Count to tell the number of objects.
Numbers to 100 / K.CC.1Count to 100 by ones and by tens. / 1.1 Count to 100 by ones. / Write
Represent
T6:
Hundred chart, row, Column, Count by 10’s / Topic 6
Numbers to 100
K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). / 2.0 Count forward from a given number.
K.CC.4. Understand the relationship between numbers and quantities; connect counting to cardinality. / 3.1. Write numbers from 0 to 20.
3.2 Represent a number of objects from 0 to 20.
a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. / 4.0 – 5.0 Count objects
b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. / 4.a. Count each object in order with correct number name.
c. Understand that each successive number name refers to a quantity that is one larger. / 4.b.1. Understand that the last number name said tells how many objects altogether.
4.b.2. Understand that the rearrangement of objects does not change the total number of objects.
4.b.3 Understand that the number of objects does not change regardless of which object gets counted first.
Operations and Algebraic Thinking
Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from / K.OA.1. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. / 1.1Represent addition. / Represent
Compose
Solve
Memorize
T7:
join, number story, plus sign addition sentence, in all, altogether, add, equal sign, sum / Topic 7
Addition
K.OA.2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. / 2.1 Solve addition word problems.
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 record the answer with a drawing or equation. / 4.0 Compose numbers that make 10.
K.OA.5. Fluently add and subtract within 5. / 5.1 Memorize addition facts.
Geometry
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
Analyze, compare, create, and compose shapes.
Geometry / 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. / 1.1 Describe the shape of objects.
1.2 Describe the positions of objects. / T:14
Square, Rectangle, Triangle, Circle, Cube, Cone
T:15
Inside(in)
Outside (out)
Above (over) Below(under)
Left, Right
Behind, On (top of)
Beside, Next to
In front of
T:16
Same size,
Same shape,
Roll
StackSlide / Topic 14
Identify and Describing shapes
Topic 15
Position and Location of Shapes
Topic 16
Analyzing, Comparing, and Composing Shapes
K.G.2. Correctly name shapes regardless of their orientations or overall size. / 2.0 Name shapes.
K.G.3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”). / 3.0 Identify shapes as flat or solid.
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). / 4.1 Analyze flat and solid shapes.
4.2 Compare flat and solid shapes.
K.G.5. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. / 5.1 Model shapes.
5.2 Draw 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?” / 6.0 Compose larger shapes.
Review Numbers 0-100, Shapes, And Addition
and/or
Frontload or Begin Teaching Subtraction / Review Topics 6, 7, 14, 15, 16 and/or Frontload or Begin Teaching Topic 8
Benchmark
2
Instructional Period 3
The Focus is
Subtract and Solve Word Problems within 10 and Subtract Fluently Within 5