• Develops a beginning understanding of number, number names, and numerals
  

Students practice verbal counting along with one-to-one correspondence in counting collections of objects. We are also working on perceptual subitizing in which students recognize the quantity of a small group of objects without using other mathematical processes. Using both dot cards and ten frame arrangements, teachers should start with quick looks to 3, then move to 5, and eventually to 10.
The numeral symbol is very abstract, so the association of this symbol (numeral) with the quantity will be repeated in multiple activities. Invite parents to play games by rolling and counting spaces to practice these beginning counting ideas.

• Estimates and compares numbers in a set
  

Although we are focusing on counting sets of objects, we integrate comparison questions such as: “Which set has more?” followed by “A lot more?” or “Just a little more?” Teachers should continue to ask comparative questions when sets differ by a large amount and when sets are close in number. Assess how students compare. Can a child see only the set that has more, or do they match items from each set?

• Adds and subtracts numbers and begins to construct sets
  

These standards are addressed in Unit of Study 2.

• Estimates and compares lengths

Several activities focus on measuring people (height) and steps (length). Students begin by describing an attribute with the correct vocabulary (tall/short, long/short) then move to directly comparing, to measuring, and to quantifying and comparing measurements: Who is taller? (vocabulary); Stand back to back (directly comparing); Measure with hands (counting non-standard units).

• Identifies common attributes, patterns and relationships

Patterning activities are integrated through fine motor activities, such as making a friendship bracelet.

Students sort data to make sense of a set and answer questions. Sorting activities are important for many areas in learning, especially in counting. After sorts are made, teachers should integrate questioning around cardinality (how many?) and comparison (which set
has more?).

• Explores concepts of geometry and spatial relationships

In learning about their environment, students will use positional words to describe objects and places. Be precise in asking students to place objects. Say, “Please put the pencil next to the red marker” versus “Put the pencil over there.”

In addition, we will use quick looks to build the visual part of the brain. Ask questions such as, can you imagine...? to force the mind to see something that the eyes have yet to see.

Make sure that puzzles, tiles, and blocks are on math shelves throughout the year to help build spatial relationships and provide opportunities to turn/rotate, flip/reflect, and to see smaller shapes that make up larger shapes.

• Develops  a beginning understanding of number, number names, and numerals

In UOS3 teachers use “quick look” cards to help students subitize numbers. Students show  quantities by holding up fingers or matching the number by building an equivalent set  on a ten frame. When working with quick looks, teachers should eventually decrease the  time each card is shown to students from three seconds to one or two seconds and notice  if students are subitizing or counting quantities. Lessons throughout UOS3 provide ample  opportunities for students to practice counting. The goal is for students to understand that  the last number counted represents the total. Note that students should be given time to  self-correct errors when counting. Teachers can extend learning by asking students to make  an equivalent set after counting a set and identifying the amount. Teachers should notice  how students organize items for counting. By changing arrangements when students are  counting, teachers help children discover that the same quantity can be represented in  different ways. When students count, teachers should observe to see if students “count  all” or “count on.” By allowing children time to explain their thinking and compare it to the  thinking of others, teachers help students discover more efficient ways of counting.

• Estimates and compares numbers in a set

With abundant counting practice in UOS3, teachers should provide students opportunities  to compare the quantities of sets after counting. Additionally, teachers should model the  use of terminology (“more”/“less,” “how many more”/“how many less,” and “most”/“least”)  and encourage students to use this math-specific language when comparing sets.  Students also explore the concept of ordinal numbers and practice the use of sequential  language (“first,” “next,” “then,” and “last”) in UOS3 lessons. Teachers are encouraged to find  opportunities throughout the school day to incorporate these skills into students’ daily  routines: Who is first/last in line? First, we will wash our hands; Next, we will eat lunch; Will  you put your jacket on the second hook? etc.

• Adds and subtracts numbers and begins to construct sets

In UOS3 students explore combining sets by identifying the sum when shown two quick  look subitizing cards. Teachers should encourage students to explain their thinking, e.g., “It’s  four because I saw two and two.” Teachers also should notice if students are counting all,  counting on, or subitizing the total.  

In addition, students have opportunities in UOS3 to view part/whole relationships when  working with dice and with ten frames to view different representations of numbers: “I saw six  dots, three on each side” or “I saw six dots, four on the top and two more on the bottom,” etc.

• Estimates and compares lengths 
  

Students explore comparative length in UOS3 by building and comparing the heights of  towers. Teachers model the use of comparative measurement language (“taller”/“tallest,”  “shorter”/“shortest”) and encourage students to use it when comparing heights.

• Identifies common attributes, patterns,  and relationships 
  

UOS3 provides multiple opportunities for students to classify objects according to  similarities and differences as well as to sort groups of objects based upon attributes.  Students should be encouraged to name the attribute by which they are sorting and can be  challenged to think more deeply by sorting the same collection of objects/pictures in more  than one way. Teachers should encourage children to use specific language to describe  relationships (“I noticed that these items are similar/different because…”) and notice ways  they incorporate this language and thinking in daily classroom conversations.  

Students explore patterns in UOS3 by describing, extending, and duplicating patterns,  as well as by identifying pattern units. Students are asked to demonstrate knowledge of  patterning by creating an example and a non-example of a pattern.  

Teachers should move students from identifying and extending repeating units in patterns  to applying them in a puzzle such as a maze. Additionally, teachers should continue to  encourage students to find patterns in their daily lives.

• Explores concepts of geometry and spatial relationships

Geometry concepts are reinforced and practiced in UOS3 through puzzle activities. Students  are given opportunities to identify shapes and describe their attributes and to manipulate  shapes to complete puzzles. Teachers should model for students the use of geometric  language such as “rotate”/“turn,” “flip”/“reflect,” and “slide” as students move shapes to fit  in the puzzles. Children should be encouraged to use similar language when transforming  shapes to make them fit into the puzzle. When discussing shapes, teachers may model for  students how shapes can be combined to create composite shapes. When students are ready  for a challenge, teachers should introduce new shapes into a puzzle design.

• Develops  a beginning understanding of number, number names, and numerals

Number standards are practiced and reinforced throughout UOS5. Children have ample practice counting sets, matching numerals to quantities, and subitizing. Students practice quickly identifying quantities presented in different formats (dots, ten frames, fingers, tally marks). The learning is extended by asking children to make sets that are equivalent to a given set. Teachers should take note of how students count (in groups, subitizing, one by one) to assess where students are along the learning trajectory. The tasks in UOS5 challenge students to count objects on a picture which presents more of a challenge because children have to keep track of counted objects, rather than moving them around. Lessons requiring students to sequence events provides children with opportunities to use ordinal numbers.

• Estimates and compares numbers in a set

Activities in UOS5 requiring students to sort objects by different attributes provides opportunities for  children to compare sets using the terms more/less. The learning is extended by asking students how  they can make the quantities the same (“How many would I need to add or take away to make these  sets the same?”). Students continue to practice estimating quantities of sets by comparing them to a  benchmark set of five or ten. (For example, children are shown a group of five or ten objects then asked  to determine if their set is more or less than five or ten.) Students are guided to make predictions from  their estimates and to self-evaluate their predictions based on data.

• Adds and subtracts numbers and begins to construct sets

Number concepts are further developed in UOS5 through activities in which students combine or  separate sets and change quantities in sets by adding or removing items. Quick look routines provide  opportunities for children to practice seeing numbers in different groupings. Through working with a  ten frame children explore the part-part-whole relationship of ten. Students count quantities in pictures  and practice solving joining/separating stories. (“How many butterflies do you see in this picture? I  wonder how many there would be if one more joins the group.”)

• Estimates and compares lengths 
  

In this unit, students continue to practice comparative measurement using the math vocabulary of  taller/shorter and by ordering objects by length. Students also explore measurement by comparing  the lengths of objects to a non-standard measurement unit. (“Is it taller or shorter than the ten-stick?”) Teachers encourage accuracy with measurement by guiding students to align the end of the measuring  unit evenly with the base of the object and to place units end to end with no gaps.

• Identifies common attributes, patterns,  and relationships 
  

Literature provides a springboard for students to identify the common attributes of plants and to  sort objects and pictures accordingly. Children are challenged to identify things that don’t belong in  a picture and to suggest ways to change an item so it would belong. Students continue to practice  building and identifying patterns with increased complexity. UOS5 lessons extend the thinking by  asking students to identify the pattern unit within a given pattern and to record a pattern after building  it. Teachers challenge students to dig deeper by asking them to build a pattern with a single item,  encouraging them to focus on the orientation of the object.

• Generates and answers questions in the natural environment
  

Data representation is a key concept in UOS5. Students represent data concretely by building a class  graph with stacking cubes, then transfer this data to an individual graph. Students graph predictions  and learn to make tally marks to record data they gather about plant heights. Through questioning,  teachers encourage students to interpret and describe the data on their graphs.

• Explores concepts of geometry and spatial relationships

Students continue to explore concepts of geometry in UOS5. Through the study of butterflies, children  explore the concept of symmetry using mirrors for free exploration. Students then move to creating  symmetrical designs and identifying examples of symmetry in nature. Lessons in UOS5 provide  opportunities for students to continue exploring 2-D and 3-D shapes and their attributes. Teachers  incorporate geometry into their daily routines by continuously encouraging students to find shapes in  their environment and to describe the attributes that help them to identify the shapes they are seeing.  Teachers are encouraged to model precise terminology with students. For example, when a child  identifies a cube as a square, say, “Yes, you do see a square on one of the faces of this cube. It has six  faces that are squares.”