Unit Overview
Students will begin developing a sense of cardinality through counting and representing a numeral with objects. Counting objects is important for students learnthe connection of numbers to quantity, rather than rote “sing-song” counting practice. Through these counting activities, students will build 1:1 correspondenceof number name to numeral. Counting activities include practice counting out quantities of objects and beginning to see small amounts of objects as a group. In addition, they learn that, when counting, the last number said tells the total number of objects in the set.
From saying the counting words to counting out objects. Students usually know or can learn to say the counting words up to a given number before they can use these numbers to count objects or to tell the number of objects. Students become fluent in saying the count sequence so that they have enough attention to focus on the pairings involved in counting objects. To count a group of objects, they pair each word said with one object.K.CC.4a
Students combine two-dimensional shapes and solve problems such as deciding which piece will fit into a space in a puzzle, intuitively using geometric motions (slides, flips, and turns, the informal names for translations, reflections, and rotations, respectively). They can construct their own outline puzzles and exchange them, solving each other’s.
Kindergarten comes to a close with another opportunity for students to explore geometry in Module 6. Throughout the year, students have built an intuitive understanding of two- and three-dimensional figures by examining exemplars, variants, and non-examples. They have used geometry as a context for exploring numerals as well as comparing attributes and quantities. To wrap up the year, students further develop their spatial reasoning skills and begin laying the groundwork for an understanding of area through composition of geometric figures.
Connection to Prior Learning
Prior to kindergarten, students may have had practice counting aloudto practice the counting sequence. They may have been exposed to songs or finger playsthrough pre-school or educational television programs. Through free play, children may have experience counting objects in such activities as setting the tableor sharing toys or food. They may also gain background experience by helping adults or following directions, such as “Please go get me 5 napkins.” Or “Bringyour two shoes over here.” Kindergartners develop a sense of quantity through repetitive practice as they explore a variety of routines. During the first unit, students have been exposed to various classroom routines that involve counting.
Major Cluster Standards
Count to tell the number of objects (0-10 objects)
K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
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.
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.
c. Understand that each successive number name refers to a quantity that is one larger.
Major Cluster Standards Unpacked
K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
Students count a set of objects and see sets and numerals in relationship to one another. These connections are higher-level skills that require students to analyze, reason about, and explain relationships between numbers and sets of objects. The expectation is that students are comfortable with these skills with the numbers 1-20 by the end of Kindergarten.
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. Students implement correct counting procedures by pointing to one object at a time (one-to-one correspondence), using one counting word for every object (synchrony/ one-to-one tagging), while keeping track of objects that have and have not been counted. This is the foundation of counting.
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. Students answer the question “How many are there?” by counting objects in a set and understanding that the last number stated when counting a set (…8, 9, 10) represents the total amount of objects: “There are 10 bears in this pile.” (cardinality). Since an important goal for children is to count with meaning, it is important to have children answer the question, “How many do you have?” after they count. Often times, children who have not developed cardinality will count the amount again, not realizing that the 10 they stated means 10 objects in all. Young children believe what they see. Therefore, they may believe that a pile of cubes that they counted may be more if spread apart in a line. As children move towards the developmental milestone of conservation of number, they develop the understanding that the number of objects does not change when the objects are moved, rearranged, or hidden. Children need many different experiences with counting objects, as well as maturation, before they can reach this developmental milestone.
c. Understand that each successive number name refers to a quantity that is one larger. Another important milestone in counting is inclusion (aka hierarchal inclusion). Inclusion is based on the understanding that numbers build by exactly one each time and that they nest within each other by this amount. For example, a set of three objects is nested within a set of 4 objects; within this same set of 4 objects is also a set of two objects and a set of one. Using this understanding, if a student has four objects and wants to have 5 objects, the student is able to add one more- knowing that four is within, or a sub-part of, 5 (rather than removing all 4 objects and starting over to make a new set of 5). This concept is critical for the later development of part/whole relationships. Students are asked to understand this concept with and without (0-20) objects. For example, after counting a set of 8 objects, students answer the question, “How many would there be if we added one more object?”; and answer a similar question when not using objects, by asking hypothetically, “What if we have 5 cubes and added one more. How many cubes would there be then?”
Additional Cluster Standards
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-Spaghetti and Marshmallows) and drawing shapes.
K.G.6Compose simple shapes to form larger shapes. For example, “Can you joint these two triangles to make a rectangle?:
Additional Cluster Standards Unpacked
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.
Students relate one shape to another as they note similarities and differences between and among 2-D and 3-D shapes using informal language.
For example, when comparing a triangle and a square, they note that they both are closed figures, have straight sides, but the triangle has 3 sides while the square has 4. Or, when building in the Block Center, they notice that the faces on the cube are all square shapes.
Kindergarteners also distinguish between the most typical examples of a shape from obvious non-examples.
For example: When identifying the triangles from a collection of shapes, a student circles all of the triangle examples from the non-examples.
K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls-Spaghetti and Marshmallows) and drawing shapes.
Students apply their understanding of geometric attributes of shapes in order to create given shapes. For example, students 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.
Because two-dimensional shapes are flat and three-dimensional shapes are solid, students may draw or build two-dimensional shapes and only build three-dimensional shapes. Shapes could be built using materials such as clay, toothpicks, marshmallows, gumdrops, straws, pipe cleaners, etc. Students should understand and identify two-dimensional shapes used to construct three-dimensional shapes.
K.G.6Compose simple shapes to form larger shapes. For example, “Can you joint these two triangles to make a rectangle?:
This standard 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 move, rotate, flip, and arrange puzzle pieces to complete a puzzle. Kindergarteners use their experiences with puzzles to use simple shapes to create different shapes.
For example, when using basic shapes to create a picture, a student flips and turns triangles to make a rectangular house.
Students also combine shapes to build pictures. They first use trial and error (part a) and gradually consider components (part b).
Focus Standards for Mathematical Practice
MP.1 Make sense of problems and persevere in solving them. Students persist in their use of trial and error until they begin to use the attributes of a puzzle to determine which shape fits into an open space. “The empty space has a long side like my triangle. Let’s see if my triangle fits.”
MP.4 Model with mathematics. Students use shapes to create pictures of common objects and use straws and clay to create models of two- and three-dimensional objects in their environment.
MP.6 Attend to precision. Ordinal numbers provide students with vocabulary to precisely describe the spatial organization of ten shapes in a straight line.
MP.7 Look for and make use of structure. Students make use of their understanding of a shape’s attributes to build three-dimensional shapes from two-dimensional shapes.
Understandings
- Counting is used to find how many or how much a quantity represents.
- The last number said when counting a quantity of objects, is the total number of objects in that group.
- The total number of objects is represented with a numeral.
- Counting one more will be the next larger number.
- Shapes can be used to build pictures, designs and other shapes.
- Shapes can be built from components.
Essential Questions
- Why do we count?
- How is number order helpful to us?
- What can numerals represent?
Prerequisite Skills/Concepts:
- Recall hearing/seeing others rote count and count objects.
- Identify “first” and “last” related to order or position.
- Analyze, compare, and sort two- and three-dimensional shapes and objects, in different sizes, using informal language to describe their similarities, differences, and other attributes (e.g., color, size, and shape).
- Create and build shapes from components (e.g., sticks and clay balls).
- Count objects with one to one correspondence above 20.
- Begin predicting, “What’s next?” when asked about the next number in a sequence.
Knowledge: Students will know…
- Names for numerals.
- Sequence and order of counting numbers.
- Use one-to-one correspondence when counting. (K.CC.4)
- Know and say the standard order when counting. (K.CC.4)
- Name the next number in a counting sequence. (K.CC.4)
- Analyze and compare 2 and 3-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts, and other attributes. (K.G.4)
- Model shapes in the world by building shapes from components and drawing shapes. (K.G.5)
- Use smaller shapes to make bigger shapes or pictures. (K.G.6)
Transfer of Understanding
- Number recognition to count objects and pictures, or count out appropriate quantities of objects in real-world situations.
- Sense of quantity to recognize that the number of objects is the same regardless of the arrangement. For example a group of 6 objects is the same quantityregardless of whether they are scattered or arranged in a line, circle, rectangle, die or domino pattern.
Academic Vocabulary
- First, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth (ordinal numbers)
- Above, below, beside, in front of, next to, behind (position words)
- Circle
- Cube (three-dimensional shape)
- Cylinder (three-dimensional shape)
- Face (two-dimensional side of a shape )
- Flat (two-dimensional shape)
- Hexagon (flat figure enclosed by six straight sides)
- Rectangle (flat figure enclosed by four straight sides)
- Solid (three-dimensional shape)
- Cone (three-dimensional shape)
- Sphere (three-dimensional shape)
- Square (flat figure enclosed by four straight, equal sides)
- Triangle (flat figure enclosed by three straight sides)
Unit Resources
Pinpoint: Kindergarten Unit #6
Routines and Centers
Know number names and the count sequence.
K.CC.1 Count to 100 by ones and tens
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)
K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.
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.
Connections to Subsequent Learning
Students in Kindergarten will apply knowledge of pattern in numbers 0-10 to count and quantify numbers up to 20. They will use understanding of numbers 0-10 to develop knowledge of teen numbers as “ten and some more.” In future units, students will practice counting by 10s, once they have mastered the counting sequence counting by ones.