/ JORDAN SCHOOL DISTRICT
Curriculum and Staff Development
Elementary Mathematics
(801) 567-8319
Utah Core Standards Mathematics
Kindergarten
This scope and sequence is aligned with the pacing of the Jordan School District adopted text,
Math Expressions, a product of Houghton Mifflin Harcourt (HMH). This is done for several reasons:
  1. FOCUS ON THE CORE: All teachers are able to stay focused on the Utah Core Standards throughout a unit. (While the text is aligned to the core, we are not teaching the text. We are teaching the core.)
  1. TEXTBOOK USE IS OPTIONAL: Teachers wishing to use their own resources and strategies are able to quickly locate core content for each unit without having to search through the textbook for correlations.
  1. PLC SUPPORT: Teachers using the textbook and those using other resources are able to continue to collaborate in PLC’s because they’re all working on the same content.

IMPORTANT VOCABULARY:

The term UNIT refers to the Math Expressions “unit”.

The term BLOCKrefers to an assessment period ranging from two to five weeks. These assessment periods serve as checkpoints for determining student mastery of core content and mathematical practices and are followed up by RTI based instruction.

The term BENCHMARK alsorefers to an assessment period. A benchmark is comprised of three blocks. Grades K-2 have four benchmarks and grades 3-6 have three benchmarks across the year. These assessment periods serve as checkpoints for determining student mastery of core content and mathematical practices and are followed up by RTI based instruction.

The term CLUSTER refers to groups of related standards.

The term STANDARD refers to the numbered and lettered items within a cluster. They are the focused mathematics that students should know (conceptual understanding), do (procedural understanding), and show (representational understanding).

The term DOMAIN refers to larger groups of related standards. They contain standards organized around clusters. Some domains have multiple clusters.

NOTE ABOUT SELECTED VOCABULARY: The Potential Vocabulary section of this document provides many possible vocabulary words for the unit. Be selective about the words your students need from this list.

PRIMARY / CONNECTING FOCUS OF A UNIT: The primary focus should take approximately 80% of your instruction time over the course of the unit. The connecting focus is provided so that students begin to see the interrelated strands within mathematics and should take approximately 20% of your instruction time.

Support materials are available at

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The Curriculum and Staff Development Department exists to provide support and professional development for administrators, teachers, and the school community in evidence-based best practices through a collaborative, interdisciplinary, and unified approach for increased student achievement and organizational effectiveness. / How do the Utah Core Standards support our work as teachers in Jordan School District?
The Utah Core provides content and practice standards for teachers to guide their work as Professional Learning Communities. PLCs are “educators committed to working collaboratively in ongoing processes of collective inquiry and action research to achieve better results for the students they serve. Professional Learning Communities operate under the assumption that the key to improved learning for students is continuous job-embedded learning for educators” (DuFour, 2004).
PLC’s focus on 3 BIG IDEAS…
  1. FOCUS ON COLLABORATION
  2. FOCUS ON LEARNING
  3. FOCUS ON RESULTS
JSD & State documents support teachers in their PLC conversations as they discuss the 4 BIG QUESTIONS:
  1. What do WEwant our students to know and be able to do?
  • Utah Core Standards ~ content standards
~ Scope and Sequence
~ Vocabulary Cards
~ USOE Core Curriculum Guides
  • Utah Core Standards ~ practice standards
~ Practice Standards Posters for Students
*The Math Expressions textbook is an additional resource for teaching the content and practice standards.
  1. How will WE know if our students know it and/or can do it?
  • Common Formative Assessments
  1. What will WE do if they do not know it and/or cannot do it?
  • Intervene and Re-teach
  1. What will WE do if they do know it and/or can do it?
  • Enrich and Accelerate

Tier 3

  • Tier 3 instruction replaces Tier 2, and is in addition to Tier 1, for students who did not respond to Tier 2 instruction.
  • 30 minutes of intense, daily, targeted, explicit instruction with an emphasis on student needs (individual or small groups).
  • Emphasis on essential knowledge and skills of numbers and operations.
  • Development of mathematics vocabulary.
  • Instructional methods explicitly link concepts and skills with physical, visual, and abstract representations.
  • Weekly progress monitoring, diagnostic assessments and formative assessments.
  • Communication with the school and parents regarding student progress and needs.

Tier 2

  • 30 minutes of daily, targeted, systematic, explicit instruction (small groups).
  • Instruction focused on Critical Areas as identified in Utah Core Mathematics Standards.
  • Strategies include, but are not limited to,additional support with Practice Standards, conceptual development of core mathematical ideas

and skills, explicit connections between physical, visual, and abstract representations, guided practice, and mathematics software.

  • Math Expressions instructional materials are possible resources for Tier II instruction.

Tier 1 All Students

  • 60 minutes of daily Tier I instruction in the grade level Utah Core Mathematics Standards: Content AND Practice Standards.
  • Instructional strategies include, but are not limited to, whole-class conceptual development of core grade level mathematics,

differentiated instruction, guided practice, use of physical, visual, and abstract representations, manipulatives, technology, and

applications of skills throughout the day across content areas.

  • Teachers use the recommended JSD Scope & Sequence.
  • At the end of every unit or block of instruction teachers formatively assess student progress using the JSD assessment

recommendations, which include Math Expressions and benchmark assessments.

  • At the end of three blocks of instruction, teachers formatively assess student progress using JSD Benchmark

Assessments. Results of these assessments are given to the principal and the JSD Curriculum Office.

  • JSD primary elementary mathematics text is Math Expressions.
  • Teachers identify learning targets that are not being achieved andengage struggling students in Tier 2 intervention

Kindergarten Critical Content Areas
In Kindergarten, instructional time should focus on two critical areas:
Critical Area 1: Representing, relating, and operating on whole numbers, initially with sets of objects
Students use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set; counting out a given number of objects; comparing sets or numerals; and modeling simple joining and separating situations with sets of objects, or eventually with equations such as 5 + 2 = 7 and 7 – 2 = 5. (Kindergarten students should see addition and subtraction equations, and student writing of equations in kindergarten is encouraged, but it is not required.) Students choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the cardinalities of small sets of objects, counting and producing sets of given sizes, counting the number of objects in combined sets, or counting the number of objects that remain in a set after some are taken away.
Critical Area 2: Describing shapes and space. (More learning time in kindergarten should be devoted to number than to other topics.)
Students describe their physical world using geometric ideas (e.g., shape, orientation, spatial relations) and vocabulary. They identify, name, and describe basic two-dimensional shapes, such as squares, triangles, circles, rectangles, and hexagons, presented in a variety of ways (e.g., with different sizes and orientations), as well as three-dimensional shapes such as cubes, cones, cylinders, and spheres. They use basic shapes and spatial reasoning to model objects in their environment and to construct more complex shapes.

DAYS IN BENCHMARK Kindergarten

Kindergarten / B1 / B2 / B3 / B4 / Total Days
A-track / 41 / 43 / 46 / 19 Days, K testing + 9 more days / 158
B-track / 39 / 41 / 42 / 19 Days, K testing + 15 more days / 156*
C-track / 40 / 43 / 46 / 17 Days, K testing + 10 more days / 156*
D-track / 36 / 41 / 46 / 23 Days, K testing + 10 more days / 156*
Traditional / 39 / 43 / 44 / 28 Days, K testing + 9 more days / 163**
Math Expressions Units / Unit 1 and first half of unit 2 / Second half of unit 2 and unit 3 / Unit 4 and first half of unit 5 / Second half of unit 5
Domain / Cluster
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.
BENCHMARK 1 ~ Block 1
Math Expressions Unit 1: Lessons 1-6 / Math Routines, Counting and Cardinality 1-5(7-12 Days): For specific days according to tracks please refer to 2012-2013 Unit and Benchmark schedules / Kindergarten
CONTENT Standards
PRIMARY / CONNECTING FOCUS OF A UNIT: The primary focus should take approximately 80% of your instruction time over the course of the unit. The connecting focus is provided so that students begin to see the interrelated strands within mathematics and should take approximately 20% of your instruction time.
PRIMARY FOCUS OF UNIT: Counting and Cardinality
Know number names and the count sequence.
2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
Count to tell the number of objects.
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.
Potential Vocabulary: number, counting, zero, one, two, three, four, five, partners, group, scene,
Recommended Formative Assessment for block 1: Due to Kindergarten screening no formative assessment is recommended for block one, however, you may complete the pre-assessment during screening.
PRACTICE Standards
Math Sense Making
1. Make sense of problems and persevere in solving them.
6. Attend to precision. / Math Talk
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others. / Math Drawings
4. Model with mathematics.
5. Use appropriate tools strategically. / Math Structure
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
I Can Statements
PRIMARY FOCUS
  • I know number names and the count sequence for numbers 0-5
  • I can count to 10 by ones.
  • I can count forward beginning from any given number.
  • I can write and name numbers 0 - 5.
  • I can write a number to tell how many objects are in a set up to 5.
  • I know that when I count I use one number name for each object.
  • I know that when I count the last number name tells the number of objects counted.
  • I know that the number of objects in a group stays the same regardless of how I arrange them.
  • I can count 5 objects in a line, a circle, or in an array.
  • I can count 5 objects scattered in a pile.
  • I can count out a given number of objects 1- 5.

BENCHMARK 1 ~ Block 2
Math Expressions Unit 1: Lessons 7-18 / Adding, Subtracting, and Comparing Through 5, Show and Practice Numbers Through 10 (14-15 Days) / Kindergarten
CONTENT Standards
PRIMARY FOCUS OF UNIT: Counting and Cardinality
Know number names and the count sequence.
1. Count to 100 by ones and by tens.
2. Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
3. Write numbers from 0 to 20. Represent a number of objects with a written numeral 0 to 20. Represent a number of objets with a written numberal 0 – 20 (With 0 representing
a count of no objects).
Count to tell the number of objects.
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.
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.
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.
PRIMARY FOCUS OF UNIT: Operations and Algebraic Thinking
Understand addition as putting together and adding to, and under- stand subtraction as taking apart and taking from.
  1. Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.
  2. Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.
CONNECTING FOCUS: Measurement and Data
Classify objects and count the number of objects in each category.
3.Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.
CONNECTING FOCUS: Geometry
Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
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.
2. Correctly name shapes regardless of their orientations or overall size.
3. Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”).
Analyze, compare, create, and compose shapes.
  1. 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).
  2. Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Potential Vocabulary: visualize, partners, circle, flat shape, above, below, beside, behind, in front of, next to, compare, vertical, horizontal, taller, more, shorter, less, longer, left, right, rectangle, square, side, corner, fewer, pair, group, same, alike, different, order, straight line, diagonal,
Recommended Formative Assessment for Block 2: Complete Review/Test for Unit 1 (Exercises 1-10). Teachers may choose to complete the assessment over 1-3 days. It may be completed as a whole class or in a small group.
PRACTICE Standards
Math Sense Making
1. Make sense of problems and persevere in solving them.
6. Attend to precision. / Math Talk
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others. / Math Drawings
4. Model with mathematics.
5. Use appropriate tools strategically. / Math Structure
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
I Can Statements
PRIMARY FOCUS OF UNIT
  • I know number names and the count sequence for numbers 0-10
  • I can count to 10 by ones.
  • I can count forward beginning from any given number.
  • I can write and name numbers 0 - 10.
  • I can write a number to tell how many objects are in a set up to 10.
  • I know that when I count I use one number name for each object.
  • I know that when I count the last number name tells the number of objects counted.
  • I know that the number of objects in a group stays the same regardless of how I arrange them.
  • I can count 10 objects in a line, a circle, or in an array.
  • I can count 10 objects scattered in a pile.
  • I can count out a given number of objects 1- 10.
  • I can tell if a group of objects is greater than, less than, or equal to another group of objects.
  • I can show addition using objects, fingers, mental images, drawings, sounds, situations, explanations, expressions, or equations.
  • I can show subtraction using objects, fingers, mental images, drawings, sounds, situations, explanations, expressions, or equations.
  • I can solve addition word problems (to 5) by using objects or drawings.
  • I can solve subtraction word problems (from 5) by using objects or drawings.
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  • I can break down (decompose) numbers less than or equal to 5 in more than one way.
  • I can break down (decompose) numbers less than or equal to 5 into pairs by using objects or drawings.
  • I can show number pairs with a drawing or equation.
CONNECTING FOCUS:
  • I can classify objects into given categories and count the numbers of objects in each category.
  • I can sort categories by counts.
  • I can describe objects in the environment using names of shapes.
  • I can describe the position of objects using terms such as above, below, beside, in front of, behind, and next to.
  • I can correctly name shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
  • I can name shapes regardless of size or position.
  • I can identify shapes as two-dimensional (lying in a plane, “flat”).
  • I can identify shapes as three dimensional (“solid”).
  • I can compare two and three dimensional shapes in different sizes and positions.
  • I can use informal language to describe similarities, differences, parts, and other attributes of two and three-dimensional shapes.
  • I can draw shapes in the world.
  • I can model and build shapes in the world.