Trimester Overview
In this trimester the focus is on the introduction of developing number sense, with an emphasis being on the numbers 0 through 10. The standards in the domains Counting and Cardinality (CC), Operations and Algebraic Thinking (OA), and Measurement and Data (MD) all support one another and should be taught interrelated. The CC standards are the understanding of numbers and the OA and MD standards are the applications that help develop the CC understandings. All of these standards make up the foundation of number sense and will be continued throughout the school year.
The minor focus this trimester is identifying the shapes: square, circle, triangle, rectangle, hexagon, cube, cone, cylinder, and sphere. Once the names of these shapes are introduced, they should be used throughout the school year and recognized in everything that you do.
Focus Common Core State Standards for Mathematical Content:
K.CC.1: Count to 100 (20) by ones and by tens.
K.CC.3: Write numbers from 0-20 (10). Represent a number of objects with a written numeral 0-20 (10) (with 0 representing a
count of no 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.
K.CC.5: Count to answer “how many?” questions about as many as 20 (10) 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 (10), count out that many objects.
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.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 (5), e.g., by using objects or drawings to
represent the problem.
K.OA.3: Decompose numbers less than or equal to 10 (5) 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.MD.3: Classify objects into given categories; count the number of objects in each category and sort the categories by count.
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.
Focus Common Core State Standards for Mathematical Practice:
MP 1: Make sense of problems and persevere in solving them.
MP 2: Reason abstractly and quantitatively.
MP 3: Construct viable arguments and critique the reasoning of others.
MP 4: Model with mathematics.
MP 5: Use appropriate tools strategically.
MP 6: Attend to precision
MP 7: Look for and make use of structure
MP 8: Look for and express regularity in repeated reasoning.
Enduring Understandings:
· Numbers are symbols that we use to represent quantities of items and are ordered from least to greatest.
· Everything can be counted. Number names tell us how many objects are in groups and allow us to count in order and compare groups of objects.
· Students can use numbers to represent quantities, to combine quantities and to find the difference of quantities.
· It is important to be able to count, order, add and subtract numbers in order to solve real life problems.
· A category is a group of objects that have similar attributes.
· Students can look at categories and figure out which has less than or equal to 10.
· A shape is the outline of an object.
· Students can identify a square, circle, triangle, rectangle, hexagon, cube, cone, cylinder, and sphere.
· Geometry helps us describe, represent, and make sense of our environment.
· Students will be able to explain their mathematical thinking by using critical thinking skills and making connections with mathematical relationships.
· Different strategies and using different tools can yield the same results.
· Being able to communicate number sense by choosing appropriate types of numbers and operations are essential skills for real world applications.
· Flexibility in thinking about numbers is a hallmark of number sense.
Essential Questions:
· What are the numbers from 0 to 20?
· How can I count forward starting at 0 or 1 up to 20?
· How can I write numbers up to 10 and show numbers of objects from 0 to 10?
· What is the connection between numbers and quantity?
· How can I count objects saying the number names in order?
· When I count objects, how can I identify the total number counted?
· How can I count, up to 10, the same amount of objects arranged in a line, a rectangular array or a circle?
· How can I count, up to 10, objects arranged in a scattered configuration?
· How can I use matching and counting strategies to identify which number is larger, smaller, or to tell if two groups have the same amount of objects?
· How can I show adding to (joining) and taking from (separating) with objects, fingers, mental images, drawings and sounds?
· How can I solve adding to (joining), taking from (separating), and putting together/taking apart (part-part-whole) word problems with numbers within 5?
· How can I record answers to word problems by using drawings and equations?
· How can I separate numbers less than or equal to 10 into pairs in more than one way?
· How can I classify objects into categories?
· How can I count single objects and then count the categories they are in?
· What is a: square, circle, triangle, rectangle, hexagon, cube, cone, cylinder and sphere?
· Where do we see shapes in the real world?
· Why is it important to communicate mathematical thinking?
· What connections can be made between different math topics and math processes?
· What strategy is your most efficient way to solve the problem?
Vocabulary:
K.CC.1 count, number
K.CC.3 count, number, set, digits
K.CC.4 count, number
K.CC.5 count, number, set
K.CC.6 count, number, greater, less, equal, same, more, fewer
K.OA.1 addition, add, subtraction, subtract, plus +, minus -, equal =, same as, equation, more, sum, difference, left, join, total, combine, remove, one more, one fewer
K.OA.2 addition, add, subtraction, subtract
K.OA.3 decompose, equation, part, whole
K.MD.3 length, weight, attribute, classify, sort, count, category
K.G.1 shapes, square, circle, triangle, rectangle, hexagon, cube, cone, cylinder, sphere, under, over, next to, beside, in front of, between / Suggested Items in Math Toolkits:
· 5 frame (in a plastic sleeve)
· 10 frame (in a plastic sleeve and/or egg carton with one column of 2 cut off)
· Counters
Suggested Instructional Resources:
· Math Wall Cards:
o Counting Patterns
o Fact Family Fun
o Mystery Addend
o Ways to Make ____
o Part/Part/Whole
· Number Sense Routines, by Jessica Shumway
· Number Talks, by Sherry Parrish / Related enVision Topic(s):
K.CC.1 à Topics 1-6 and 9-11
K.CC.3 à Topics 1-5 and 9-11
K.CC.4 à Topics 1-6 and 9-11
K.CC.5 à Topics 1-4
K.CC.6 à Topics 1-6 and 9-11
K.OA.1 à Topics 7 and 8
K.OA.2 à Topics 7 and 8
K.OA.3 à Topics 1 and 9
K.MD.3 à Topic 13
K.G.1 à Topic 15
Suggested Literature Books:
CCSS Math Content Standard / Focus CCSS Standard(s) for Mathematical Practice (SMP) / Routines / Math Wall
K.CC.1 / SMP 1, 2, 3, 6, 7, 8 / Count how many days in school with ten frames/rods and cubes
K.CC.1, K.CC.3 / SMP 2, 3, 6, 7, 8 / ‘Counting Patterns’ math wall card* – Count off a number grid; have students write the numbers on their white boards
K.CC.1 / SMP 1, 2, 3, 6, 7, 8 / Count/Tally days of the month
K.CC.1 / SMP 6 / Number Songs (Heidi songs, Greg and Steve, Jack Hartmann, etc.)
K.CC.1 / SMP 2, 3, 6, 7, 8 / Count off a number line
K.CC.1, K.CC.4a, K.CC.4b / SMP 1, 2, 3, 6, 7, 8 / Count students, girls, boys, chairs, crayons, shoes, etc.
K.CC.3, K.CC.5 / SMP 1, 2, 3, 6, 7, 8 / Quick images (dot cards)* – have students record thinking/solutions on white board
K.CC.6 / SMP 1, 3, 6, 7, 8 / Compare two groups of objects (picture cards, dot cards, etc.)
K.OA.1, K.OA.3 / SMP 3, 6, 7, 8 / ‘Fact Family Fun’ math wall card*
K.OA.1, K.OA.3 / SMP 3, 6, 7, 8 / ‘Mystery Addend’ math wall card*
K.OA.3 / SMP 1, 2, 3, 4, 6, 7, 8 / ‘Ways to Make ____’ math wall card*
K.OA.2 / SMP 3, 6, 7, 8 / ‘Part/Part/Whole’ math wall card* – domino addition cards*
K.MD.3 / SMP 1, 3, 6 / One of These Things*
K.G.1 / SMP 1, 3, 6 / Name and identify Shapes in your environment (i.e. picture cards, posters, objects in the classroom)
* These routines can be found on the DUSD CGI website (www.dusd.net/cgi) under the kindergarten tab.
CCSS Math Content Standard / Focus CCSS Standard(s) for Mathematical Practice (SMP) / Lesson and/or Activity
K.CC.1, K.CC.3, K.CC.4, K.CC.5, K.CC.6, K.MD.3 / SMP 2, 3, 6, 7, 8 / Counting Collections*
K.CC.1, K.CC.3, K.CC.4, K.CC.5, K.OA.1, K.OA.2, K.OA.3 / SMP 1, 2, 3, 4, 5, 6, 7, 8 / CGI Word Problems* - This trimester focus is on Put Together/Take Apart Both Addends Unknown, Join (Add to) Result Unknown, Separate (Take from) Result Unknown, Part/Part/Whole Whole Unknown (Put Together/Take Apart Total Unknown).
Other problems, including multiplication and division, can be used to encourage number sense.
K.CC.1, K.CC.3, K.CC.4, K.CC.5, K.OA.3 / SMP 3, 5, 6, 7, 8 / Number of the Day*/ Target Number*
K.CC.1, K.CC.4, K.OA.1, K.OA.3 / SMP 1, 2, 3, 6, 7, 8 / Quick Images*/ Dot Cards*/ Ten Frames*
K.CC.1, K.CC.4, K.CC.5, / SMP 2, 3, 6, 7, 8 / 1 to 1 Counting – Use counting trays, ten frames, etc., to practice counting small numbers. You can also ask questions like, “Show me 6,’ and students count out that many (with support if needed).
K.CC.1, K.CC.3 / SMP 1, 3, 6, 7, 8 / Choral Counting*
K.OA.3 / SMP 1, 2, 3, 6, 7, 8 / Rekenrek*/ Shake It Up/ Ten Wand*
K.OA.1, K.OA.3 / SMP 1, 3, 6, 7, 8 / Numbers Galore* – Different ways to represent numbers
K.G.1 / SMP 1, 3, 6 / Shape Walk/ Find a Shape – Students are asked to find a particular shape, or see what shapes they can find, around the classroom or outside the classroom.
K.G.1 / SMP 1, 3, 6 / Taped Shapes*
K.G.1 / SMP 1, 3, 6 / Stand-on Shapes*
K.G.1 / SMP 1, 3, 6 / Walking Shapes*
K.G.1 / SMP 1, 3, 6 / Shape of the Week
K.G.1, K.MD.3 / SMP 1, 3, 6 / Shape Graphs
* These lessons/activities can be found on the DUSD CGI website (www.dusd.net/cgi) under the kindergarten tab.
Revised 8-23-13