Kindergarten Strand Summaries
		The following are descriptions of the kindergarten strands in the Math Trailblazers curriculum. The descriptions provide a brief summary and a list of the concepts that are featured. This list may be used as a quick reference to the skills and concepts included in each strand. The strand summaries reflect the scope, sequence, and tone of the kindergarten curriculum. The fundamental assumption is that math concepts and skills are best acquired through active involvement in counting, measuring, sorting, comparing, graphing, and data analysis. Problem solving and communication are a constant theme throughout all the activities. Strand Summaries Numbers in Context Strands Mathematical Concept Strands Thematic Units Calendar Connections Patterns Buildings How Many? How Much? How Far? Number Sense On the Go Looking for Math in All the Right Places Geometry Crawly Creatures Numbers! Numbers! Measurement   Numbers in Context Strands The four strands in this section contain counting, estimation, data collection, and problem-solving activities to be used on an ongoing basis throughout the year. The strands are: Calendar Connections; How Many? How Much? How Far?; Looking for Math in All the Right Places; and Numbers! Numbers! Calendar Connections Strand Summary This strand is composed of three parts. Setting Up a Classroom Calendar offers a plan for a classroom calendar display area, which includes the ten frame, a monthly calendar, weather and attendance graphs, and a growing number line. Working with the calendar on a daily basis provides a meaningful context for solving problems and exploring relationships among numbers. Calendar Updates provide suggestions for new instructional emphases as the year progresses and students mature. The updates are presented in chronological order and are to be introduced throughout the year, approximately one every two weeks. Fifty Ideas for the One Hundredth Day offers suggestions for activities that focus on the benchmark number 100 prior to and during the celebration of the one hundredth day of school. Concept Focus counting by ones, fives, and tens counting forward and counting back on the calendar using a ten frame as a visual organizer comparing numbers and quantities exploring shape, color, weather, and number patterns solving addition, subtraction, multiplication, and division problem types sorting and classifying recording data using tallies and numbers creating and reading graphs exploring concepts of measurement building an awareness of time and its passage including hours, days, weeks, months, seasons, and years developing an understanding of the value of a nickel and a penny How Many? How Much? How Far? Strand Summary Data collection is an integral part of the Math Trailblazers kindergarten curriculum. Children become actively engaged in problem solving when they work with numbers that come from their own experience and are meaningful to them. Data collection activities may include sorting and classifying objects, conducting surveys, or using measurement. Data collection has the added benefit of being a natural way to integrate mathematics into multiple curricular areas. Some of the ideas for data collection activities in this strand can be linked to the calendar. Additional data collection activities can be developed as they arise naturally in the classroom context. Ideally, an opportunity for data collection should be included each week. Concept Focus counting using one-to-one correspondence making number comparisons sorting objects using Venn diagrams and real object graphs predicting the outcome of a data collection activity measuring length and width using tallies creating data tables and graphs to represent information analyzing data Looking for Math in All the Right Places: Putting Problem Solving into the Kindergarten Day Strand Summary This strand presents a conceptual framework for thinking about problem solving involving numbers. Recent research has shown that kindergarten children are capable of dealing with many different kinds of math problems. This strand helps teachers build upon an understanding of the many types of problems to design instruction that exposes children to a rich variety of problems. The strand is broken into four sections: Creating Problem-Solving Situations Through Thematic Units, Creating Problem-Solving Situations Through School Year Celebrations, Creating Problem-Solving Situations Through Children’s Literature, and Problem Solving Through Everyday Classroom Situations. Concept Focus exploring different addition, subtraction, multiplication, and division problem types communicating problem-solving strategies solving problems using manipulatives solving problems using counting strategies exploring the operations of addition, subtraction, multiplication, and division Numbers! Numbers! Strand Summary The ongoing activities and games in this strand provide practice in counting, exploring patterns, and estimating in our number system. Students make connections between different representations of numbers including ten frames, dot patterns, numerals, sign language, and concrete representations of numbers. The strand is broken into seven lessons: Counting Boxes provides a setting for children independently to count out sets to ten. Counting Bags provides children with multiple opportunities to count objects and record the number counted. Hand Counting coordinates sign language with calendar work. Oral Counting—Buzz! is a group game that provides oral counting practice. Number Books provide an opportunity for children to make connections between multiple representations of numbers. Number Race provides an opportunity for children to connect number dot patterns and symbols. In Estimation Jar children estimate the number of objects in a jar by comparing the contents of the jar to a set of objects that has a known quantity. Concept Focus using one-to-one correspondence to count sets of objects understanding that the result of counting a set of objects should be the same each time the set is counted, independent of the order in which the objects are counted connecting symbols to different representations of numbers including ten frames, number dot patterns, and counted sets developing oral and sign language counting skills discovering patterns in our number system recording used numbers developing estimation skills based on comparison to a known referent set understanding that estimates of quantities should be approximate rather than specific using the language of estimation: more than, less than, about, close to Mathematical Concept Strands This section provides core lessons that explore the topics of patterning, numbers and number relationships, geometry, and measurement. This section includes four strands: Patterns; Number Sense; Geometry; and Measurement. Patterns Strand Summary Repeating, linear patterns are explored visually, kinesthetically (using movement), and auditorily. Students are involved in a series of activities to identify and describe repeating patterns. Core patterns are described, first using object names, then using symbolic AB coding. These activities also introduce children to copying, extending, creating, comparing, and translating patterns using both manipulatives and pictorial representations. Concept Focus describing patterns by object name copying a rhythmic pattern modeled by the teacher identifying the core of a repeating, linear pattern copying a pattern using two- or three-dimensional materials extending a given pattern using corresponding materials identifying patterns using symbolic (AB) coding creating a pattern using two- or three-dimensional materials comparing patterns made from different materials translating patterns from one material to another Number Sense Strand Summary Early lessons in this strand have students counting, comparing, and ordering sets of objects. Number relationships are explored by comparing numbers to the benchmarks of five and ten and by describing numbers as more than, less than, or the same as. Model-word-symbol connections are made by playing matching games involving ten frames, dot patterns, and written numbers. Students partition numbers into smaller sets and explore the concept of “half.” Concept Focus counting objects accurately to determine the numerosity of a set comparing and ordering sets of objects describing number relationships using the language of more than, less than, and the same as developing visual representations of quantities using ten frame and number dot patterns exploring number relationships using the benchmark numbers five and ten using model-word-symbol connections exploring the part-part-whole relationship of numbers to ten exploring the relationship of fractional parts to the whole for halves and other fractions as appropriate exploring one more, two more, one less, two less Geometry Strand Summary Spatial sense is developed by giving students many experiences that focus on geometric relationships such as the direction and orientation of objects in space and on maps. The exploration of both two- and three-dimensional shapes starts by sorting and classifying objects according to their properties. The names of the shapes are introduced informally. Students also explore in a variety of ways shapes with a line of symmetry. Concept Focus understanding and using terms to describe spatial relationships using spatial terms to describe the location and position of an object using spatial terms to describe movement from one place to another applying spatial terms to a map comparing the length of paths using the terms “longest” and “shortest” developing the language to describe shapes exploring three-dimensional shapes in the environment classifying three-dimensional shapes comparing and contrasting three-dimensional shapes exploring the properties of two-dimensional shapes comparing and contrasting two-dimensional shapes investigating the relationship between two- and three-dimensional shapes organizing data in a table exploring one line of symmetry completing and creating symmetrical designs Measurement Strand Summary Students use estimation and develop measurement skills for the variables of length, area, volume, and weight (or mass). They compare and order objects according to their measurements. Measurements are made using a variety of nonstandard and standard units. In some activities, students measure the same object using different units, which helps them notice what happens when the unit changes. Measurement of time to the hour is included in this strand as students record some of the events of their day. Concept Focus estimating and comparing height comparing the size of objects ordering objects by height, capacity, and weight using the language of approximation placing units consistently and correctly estimating the number of units needed to measure revising estimates based on new information introducing the notion that the size of the unit will determine the number of units needed measuring using nonstandard and standard units constructing an understanding of the meaning of area as the number of units needed to cover a shape exploring and estimating the capacity of various containers using a two-pan balance to compare the weight of objects recording events according to the hour of the day to promote an awareness of the passage of time placing numbers in intervals representing and interpreting data in a data table and a graph Thematic Units The three units in this section are optional; they can be presented as written, modified, or used as models to develop your own thematic units. The units are: Buildings; On the Go; and Crawly Creatures. Buildings Unit Summary The mathematics in this unit emerges from activities that explore many types of buildings, with a focus on the school building and students’ homes. Children collect data by counting doors and windows, and they conduct surveys about types of homes. Students create and solve problems using an apartment building setting. The skills needed to complete this unit make it appropriate for use any time in the first semester. Concept Focus comparing and classifying data collecting, graphing, and discussing data developing concepts of length, area, and volume developing measuring skills developing concepts of geometry, such as shape recognition, symmetry, mapping, and an intuitive sense of spatial relations developing number sense using comparison creating and solving addition and subtraction problems On the Go Unit Summary The mathematics in this thematic unit emerges from the exploration of different modes of transportation. Surveys are conducted for the color of cars seen by students and the type of transportation used; toy cars are measured for their length and weight; and vehicles are sorted by attributes. The skills needed to complete this unit make it appropriate for the beginning of the second semester of school. Concept Focus sorting and classifying objects labeling and explaining sorted groups comparing the number of objects in different groups constructing picture graphs of data collected analyzing data on graphs using the language of more than, less than, and the same as placing ten numbered objects in sequential order grouping specified numbers of objects matching two items with identical numbers identifying geometric shapes estimating the space (area) an object takes comparing the use of different units for measuring length estimating weight using nonstandard units exploring the relationship between weight and size investigating the value of pennies, nickels, and dimes solving problems using coins experiencing time intervals Crawly Creatures Unit Summary Crawly Creatures develops mathematical ideas as students investigate the world of insects and spiders. They explore symmetry, shapes, partitions of numbers, and measurement. The skills needed to complete this unit make it appropriate for late in the second semester. This unit can be used earlier in the year if it is suitably modified to suit the developmental level of students in the class. Concept Focus classifying and sorting according to various characteristics tallying constructing, reading, and interpreting graphs counting and grouping objects exploring even and odd numbers informally counting by twos partitioning numbers doubling numbers solving problems involving joining and separating groups exploring the concept of multiplication and division exploring ideas of symmetry developing geometric visualization skills sequencing the days of the week exploring positions of the hour hand during a 12-hour time period measuring area using two different sizes of units     NOTE: Above text taken from Math Trailblazers Teacher Implementation Guide (TIG) Copyright © 1998 by Kendall/Hunt Publishing Company. Used with permission. Copyright © 1999 Institute for Mathematics and Science Education. All rights reserved. UIC—University of Illinois at Chicago