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Summit Math Plus Blue (K) (Independent Study)

Summit Math Plus Blue (K) (Independent Study)

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Quick Overview

This research-based course focuses on computational fluency, conceptual understanding, and problem-solving. The engaging course features new graphics, learning tools, and games; adaptive activities that help struggling students master concepts and skills before moving on; and more support for Learning Coaches to guide their students to success. The course introduces Kindergarten students to numbers through 30. Students learn through reading, writing, counting, comparing, ordering, adding, and subtracting. They experience problem solving and encounter early concepts in place value, time, length, weight, and capacity. They learn to gather and display simple data. Students also study two- and three-dimensional figures—they identify, sort, study patterns, and relate mathematical figures to objects within their environment.

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Unit 1: Shapes and Sorting

This unit focuses on describing, sorting, and classifying objects according to attributes or features. Students investigate the attributes of geometric shapes, such as circles, triangles, squares, and rectangles. They also use everyday objects, such as beads, stuffed animals, or types of fruit to improve their skills.

  • Identify Plane Figures
  • Circle, Triangle, Square, Rectangle
  • Compare Shapes
  • Compare Colors
  • Compare Sizes
  • Sizes, Shapes, and Colors
  • Sort by Color
  • Sort by Shape
  • Sort by Size
  • Sorting Different Ways


Unit 2: Shapes and Patterns

Students identify which object from a group does not belong according to the color, shape, or size of the objects. Students also learn what a pattern and a pattern core are and view different pattern types. Students begin using the letters A, B, and C to describe pattern rules AB, ABB, AAAB, AAB, ABB, ABC, and ABCC. Students identify and extend these patterns with attribute blocks and other objects.

  • Which Object Is Different?
  • AB and ABB Patterns
  • AAAB and AAB Patterns
  • ABCC and ABC Patterns


Unit 3: Numbers Through 5 and Plane Figures

Students begin by counting and grouping objects into groups of up to five, and then learn to write the numerals 1 through 5. They review triangles, squares, rectangles, and circles; learn to identify and count sides and corners—and find out that circles do not have sides or corners.

  • Count Through 5
  • Count and Show 0 Through 5
  • Write Numerals Through 5
  • Sides of a Shape
  • Corners of a Shape
  • Sides and Corners of Shapes


Unit 4: Numbers Through 10

Students begin by hearing the counting sequence of numbers from 1 through 10, and then they count aloud on their own. They represent quantities through 10 by using objects and drawings. Students then move to counting sets of 10 or fewer objects, learning that they can count the objects in any order as long as they count each item exactly one time. Students read the numbers 1 through 10 to prepare them for writing the numbers. By watching a virtual pencil, and practicing with pencil and paper, they learn to form the numbers themselves. Students learn to compare and order groups of objects, learning that numbers with greater values describe groups with more objects than numbers with lesser values. They move to comparing and ordering numbers that describe groups of objects.

  • Count Through 10
  • Show an Amount Through 10
  • Represent Amounts
  • Count Aloud Through 10
  • Show Amounts in Different Ways
  • Write Numerals 1 Through 10
  • More, Fewer, and Equal
  • Compare and Order Groups
  • Describe and Order Groups by Number
  • Write Numbers to Describe Groups


Unit 5: Calendar and Time

This unit is a review of calendars and time lessons taught throughout the first quarter. In the online Calendar/Time activities, students have learned about calendar concepts such as the names and numbers of days in a week; the notion of yesterday, today, and tomorrow; how to find a specific date on a calendar; and how many months are in a year. Students have also learned about concepts of time by studying the hours and minutes on a clock; parts of the day such as morning, afternoon, and evening; and the typical times in a day when certain activities occur.

  • Understanding Concepts of Time


Unit 6: Data and Graphs

Students learn how to compare groups of objects to determine which group has more or fewer objects, and that greater numbers are used to describe groups with more objects. Students learn to collect data and represent that data with objects, pictures, and picture graphs. They pose questions, collect data, record the results, compare, and answer questions. Students also learn to compare and answer questions about data in graphs that they have not prepared themselves.

  • Collect Data and Pose Questions
  • Ways to Show Data
  • Compare Data in a Picture Graph
  • Interpret Picture Graphs
  • Answer Data Questions
  • Analyze Data in Picture Graphs


Unit 7: Numbers Through 20

Students begin by counting groups of up to 20 objects, learning that they can count in any order as long as each item is counted once. They use models, drawings, and finally numerals to represent groups of up to 20 objects. Students then compare groups having 20 or fewer objects to determine which has more, fewer, the most, or the fewest objects. They compare numbers from 1 through 20 to determine which is more or greater, and which is lesser or fewer. They learn to write the numerals from 1 through 20.

  • Count Aloud Through 20
  • Represent an Amount Through 20
  • Count Through 20
  • Show Amounts Through 20
  • Compare Sets Through 20
  • Write Numerals Through 20
  • Compare Numbers and Sets Through 20
  • Write Numerals from 1 Through 20

Unit 8: Introduction to Addition

Students learn the meaning of addition by combining two groups of objects to find the total. By experimenting with groups of objects, they learn that changing the order in which the numbers are added does not change the sum. Students then learn to add with sums through 20 by using number lines, models, and sketches. They also learn to add by counting on by 1 and by 2 from a number.

  • Combine to Add
  • Count On to Add
  • Count On
  • Add with Models
  • Use Sketches to Add


Unit 9: Problem Solving With Addition

Students use concrete objects to solve addition story problems that involve combining groups, and explain how they are solving them. They move on to problems in which one of the groups is unknown (missing addend problems), and to checking answers to addition word problems. Students also learn how to estimate to find a sum.

  • Addition Problem Solving
  • Addition Story Problems
  • Explain Addition Solutions
  • Combine to Find Totals
  • Recognize Combine Problems
  • Missing Parts Problems
  • Estimate Sums Through 20
  • Check the Accuracy of Calculations


Unit 10: Introduction to Subtraction

In this unit, students are introduced to subtraction as taking away objects from a group of objects. They learn to take away objects and to tell how many are left, and then use sketches and countable objects to model subtraction problems and story problems. Students learn that through subtraction, they can also find out the amount of a mystery addend in an addition problem.

Students learn to apply their knowledge by using benchmarks of 5, 10, 15, and 20 to make reasonable estimates for solutions to subtraction problems. They learn that counting principles and numbers can be used to solve addition and subtraction problems and use models or sketches to check the accuracy of their solutions to subtraction word problems.

  • Take Away to Subtract
  • Subtraction as Taking Away
  • Subtract with Objects
  • Model Subtraction
  • Subtract with Pictures
  • Estimate and Check Differences


Unit 11: Problem Solving with Subtraction

Students learn to recognize and solve subtraction story problems by using concrete objects and sketches. They create their own story problems, and then solve those problems using models or sketches. They apply that knowledge to make reasonable estimates for solutions and check the accuracy of subtraction calculations.

  • Model Subtraction Stories
  • Sketch Subtraction Stories
  • Take-Away Stories
  • Compare Take-Away and Combine
  • Recognize and Solve Problems
  • Make Estimates and Check Answers

Unit 12: Subtraction as Comparison

Students use models and sketches to solve comparison subtraction problems using one-to-one- correspondence. They use pairs of numbers to create addition and subtraction problems, exploring the differences between comparing, combining, and take-away problems.

  • Compare and Subtract
  • Sketch Subtraction Problems
  • Take Away, Combine, and Compare
  • Compare to Subtract
  • Subtraction as Comparing
  • Comparison Subtraction

Unit 13: Comparison Subtraction: Story Problems

In this unit, students learn to use concrete objects to explain how to solve addition and subtraction problems involving numbers up to 10. Students also learn to recognize and solve word problems involving numbers up to 10 in which two quantities are compared by the use of addition or subtraction. Students then make estimates for solutions to subtraction problems and check the accuracy of those solutions.

  • What’s the Difference?
  • Add and Subtract Story Problems
  • Compare Quantities to 10
  • Compare: More or Fewer?
  • Compare in Everyday Situations
  • Estimate and Check Subtraction

Unit 14: Add or Subtract: Problem Solving

Students learn to recognize and solve a variety of story problems in which two quantities are combined, two quantities are compared, or one quantity changes through addition or subtraction.

  • Different Types of Problems
  • Combine and Change Problems
  • Compare and Combine Problems
  • Change and Compare Problems
  • Add or Subtract: More Exploration


Unit 15: Measurement

Students begin by finding lengths of objects using various nonstandard units, such as paperclips or beads. Then they explore measuring and comparing length, weight, and capacity.

  • Measure Objects Introduction
  • Compare Length Introduction
  • Compare Weight Introduction
  • Compare Capacity Introduction

Unit 16: Numbers Through 30

Students extend their counting ability to be able to count up through 30 objects in a group. They learn to represent amounts through 30 with objects and with sketches, and to compare groups of objects. Students determine which of two groups has more or fewer objects. They then can tell which of three groups has the fewest or the most objects. Finally, students learn to write numbers from 1 through 30.

  • Count and Show Numbers Through 30
  • Count Objects Through 30
  • Represent Amounts Through 30
  • Compare Groups Through 30
  • Groups in a Picture Graph
  • Write Numerals Through 30
  • Compare Groups and Numbers
  • Write Numerals From 1 Through 30


Unit 17: Solid Figures

Students begin by reviewing plane figures and then are introduced to some solid figures: cubes, cones, and spheres. They learn to identify these figures and to recognize them in everyday objects such as boxes and marbles. They compare the attributes of the various solids, such as the number of corners, the roundness, the color, or the size. Students identify which solid in a set of solids does not belong according to color, size, or shape.

  • Identify Solid Figures
  • More Exploration with Identifying Solid Figure
  • Compare Solid Figures by Shape or Size
  • More Exploration with Attributes of Solid Figures
  • Sort Solid Figures
  • Put Together Shapes
  • Combine Shapes: More Exploration
  • Take Apart Shapes
  • More Exploration with Taking Apart Plane Figures

Additional Information

Course Length 12 Months
Prerequisites N/A
Course Materials

Many K12 courses utilize physical materials in addition to the online content.  These materials may include the following.

Standard Kits

STANDARD kits contain K12 course materials that are required for completion of the course.  These kits include K12 authored materials and/or difficult to procure materials that a student needs to complete a course. Printed reference guides are not included in Standard kits.


CONSUMABLE kits contain only those materials from the standard kit that are intended for one time use. Families who purchase a Standard kit for Child A could later purchase a Consumable kit for Child B to complete the same course.


Offered for added convenience, ADDITIONAL kits contain easily obtained materials needed for the course which a family may already have in their home. 

Coach and/or Student Reference Guides are available for purchase with some courses.  Electronic versions of these reference guides are also available within digital courses.

Course Start Date

Independent Study Courses

Courses can be started any day for independent study courses without a teacher. Full-year courses last 12 months and semester courses last 6 months.


Courses Taught by a K12 Teacher

Courses with a teacher have designated start dates throughout Fall and Spring. Full-year courses last 10 months and semester courses last 5 months. Courses are taught by teachers in K12 International Academy. For details on start dates, click here.

Teacher Assisted This course is available in two forms: taught by a teacher or designed for independent use. This teacher-supported course is taught through K12 International Academy. It is also available as independent study, where a parent will guide the course.
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To use this course, you'll need a computer with an Internet connection.  Some courses require additional free software programs, which you can download from the Internet.

Hardware and Browsers (Minimum Recommendations)

Windows OS

  • CPU: 1.8 GHz or faster processor (or equivalent)

  • RAM: 1GB of RAM

  • Browser: Microsoft Internet Explorer 9.0 or higher, Mozilla Firefox 10.0 versions or higher, Chrome 17.0 or higher

  • At this time our users are encouraged not to upgrade to Windows 10 or Edge (the new browser)


Mac OS

  • CPU: PowerPC G4 1 GHz or faster processor; Intel Core Duo 1.83 GHz or faster processor

  • RAM: 1GB of RAM

  • Browser: Firefox 10.0 versions or higher, Chrome 17.0 or higher (Safari is not supported!)

Using  Mobile Devices with the Online School

Unfortunately, many portable devices do not support the software products required to run the Online School. These devices may include (but not limited to): Chromebooks, iPads, iPhones, iPods, Kindles, eReaders, and Andriod phones.

Internet Connections

It is highly recommended that a broadband connection be used instead of dial up.


By requesting this information, you agree to have a K12 or school representative contact you directly at the number provided, whether by person or a device that will automatically dial your home or cell phone. Consent not required for purchases.

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