• Number Concepts, Theory, Sense
• Operations
• Measurement
• Geometry
• Data Analysis/Statistics/Probability
• Patterns/Functions/Algebra
• Problem Solving/Application

Number Concepts, Theory, Sense

• Estimate, count, and represent numbers up to 99 using materials. Recognize and write numerals up to 99.
  
  • EXT: Explore number patterns beyond 99.
    
• Count backward by 1's across a decade (e.g., 62, 61, 60, 59 ...).
  
• Recognize and explain/show that a whole (object, picture, set, or number ) is made up of all its parts. Name a number in a variety of ways (e.g., 3 + 2, 8 - 3, 1 + 1 + 1 + 1 + 1, cinco, fingers on one hand are all names for 5).
  
• Read and write number words to 10.
  
  • EXT: Read and write number words to 19 in contextual settings (such as creating a book, poster, game, etc.)
    
• Understand numbers 11 to 19 as "ten and ____more."
  
• Estimate and compare sizes of groups using more than, less than, and equal to. Compare and order two-digit numbers.
  
• Identify ordinal position through tenth.
  
• Understand the concept of addition as demonstrated orally through the use of models. Explore the commutative property.
  
  • EXT: Represent addition sentences using computer software such as KidPix.
    
• Model different subtraction situations including comparison of two groups, take away, and part-part-whole.
  
• Explore the relationship between addition and subtraction by modeling and recording fact families in contextual settings.
  
• Use and explain the addition and subtraction strategies of "counting on and back" (1, 2, and 3); adding zero; using doubles and near doubles; and making ten.
  
  • EXT: Explore the strategy of using 10 (e.g., 10 +4 = 14, so 9 + 4 = 13).
    
• Explore the grouping of objects in a variety of ways (e.g., 19 can be 3 groups of six with 1 left over, 1 group of 10 with 9 left over, 3 groups of 5 with 4 left over, etc.).
  
• Model two-digit numbers by making groups of 10s and identifying the 1s left over.
  
• Exchange tens for ones and vice versa using concrete materials. Exchange pennies for dimes and vice versa.
  
• Recognize equal parts. Identify and represent the concepts of one-half and one-fourth using concrete materials.
  
  • EXT: Recognize and use the symbols to record fractional parts (1/2 , 1/4) of a region.
    
• Recognize the value of a penny, a nickel, a dime, and a quarter.
  
  • EXT: Find and record a variety of ways to show a given amount of money.

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• Write and solve one-digit addition and subtraction sentences written horizontally and vertically. Recognize and use plus, minus, and equal signs.
  
  • EXT: Add and subtract tens and ones; communicate strategies.
    
• Mentally compute addition facts, sums to 10.
  
  • EXT: Mentally compute subtraction facts, sums to 10.
    
• Estimate and add 3 addends, sums to 10.
  
• Find sums for doubles to 9 + 9. Subtract doubles to 12 - 6.
  
  • EXT: Add equal groups to explore multiplication.
    

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• Estimate, compare, and measure length using nonstandard units and inches.
  
  • EXT: Explore and identify centimeters.
    
• Explore area with concrete materials.
  
  • EXT: Explore the concept of volume by building or filling box shapes using cubes.
    
• Estimate and compare the weights of objects up to 1 pound using a balance.
  
  • EXT: Estimate and compare the weight of an object to a kilogram.
    
• Estimate and compare capacity using nonstandard containers; estimate, compare, and measure capacity in cups, pints, and quarts using physical materials.
  
  • EXT: Fill and compare containers that are more or less than a liter.
    
• Relate a given Fahrenheit thermometer reading to hot and cold.
  
  • EXT: Read a Fahrenheit thermometer and record temperature over a period of time.
    
• Recognize the value of a collection of pennies; recognize the value of a collection of nickels; recognize the value of a collection of dimes. Find the value of collections of pennies and dimes to 99¢.
  
  • EXT: Find the value of a mixed set of coins to 99¢.
    
• Relate time to daily activities. Read time to the hour; explore time to the half-hour on both digital and analog clocks.
  
• Name and sequence the days of the week. Recognize seasons and calendar patterns. Sequence time (e.g., daily schedule, classroom birthdays).
  
  • EXT: Name and sequence the months of the year.
    

• Recognize the concept of symmetry.
  
  • EXT: Identify, make, and extend symmetrical (mirror image) patterns.
    
• Recognize and identify 2-dimensional shapes (triangle, square, circle, rectangle) regardless of orientation. Explore other 2-dimensional shapes (regular and irregular polygons, and non-polygons). Sort shapes by size, shape, sides, or corners and identify sorting rule.
  
  • EXT: Create multiple sorting rules for a given set of shapes.
    
• Explore congruence, using concrete materials (e.g., geoboards, pattern blocks).
  
  • EXT: Explore the results of combining and subdividing shapes to create different shapes.
    
• Explore 3-dimensional solids in the environment.
  
  • EXT: Identify and sort 3-dimensional solids in the environment.

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• Collect, count, and sort data. Justify the sorting rule.
  
• Keep track of data by using concrete objects, tally marks, and organized lists.
  
• Organize, record, and interpret data on grids and charts.
  
• Record and interpret data on bar graphs and pictographs. Share findings.
  
• Explore probability with concrete materials (e.g., number cubes, coins, 2-colored counters, spinner) and communicate findings.
  
  • EXT: Make predictions about similar experiments based on findings (e.g., What would happen if -you were allowed more spins? -you added more cubes?)

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• Count forward by 2s, 5s, and 10s up to 100.
  
  • EXT: Count forward by 10s starting at numbers other than multiples of 10 (e.g., 26, 36, 46 ...).
    
• Identify and describe patterns in objects, places, numbers, and simple number sentences. Extend a pattern. Create patterns.
  
  • EXT: Create shape and numerical patterns using computer software and calculators.
    
• Explore the pattern of odd and even numbers.
  
• Find missing parts in part-whole situations using materials (e.g., "I have 10 M&M's; six are green and the rest are yellow. How many are yellow?").
  
• Find a simple function rule given input and output data (e.g., If the number 3 becomes 4 and 6 becomes 7, what is the function rule that caused this?). Limit the rules to +1, -1, +2, -2, and doubles.
  

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• Count forward by 2s, 5s, and 10s up to 100.
  
  • EXT: Count forward by 10s starting at numbers other than multiples of 10 (e.g., 26, 36, 46 ...).
    
• Identify and describe patterns in objects, places, numbers, and simple number sentences. Extend a pattern. Create patterns.
  
  • EXT: Create shape and numerical patterns using computer software and calculators.
    
• Explore the pattern of odd and even numbers.
  
• Find missing parts in part-whole situations using materials (e.g., "I have 10 M&M's; six are green and the rest are yellow. How many are yellow?").
  
• Find a simple function rule given input and output data (e.g., If the number 3 becomes 4 and 6 becomes 7, what is the function rule that caused this?). Limit the rules to +1, -1, +2, -2, and doubles.
  

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• Share a real-life event (math happening) and pose a question that can be answered using the information given in the story. Illustrate the number sentence by drawing a picture.
  
• Represent a verbalized (one-step addition or subtraction) story problem, using real or semi-concrete materials; record the number sentence and solve.
  
  • EXT: Sort problems by operation and/or student-generated criteria.
    
• Select appropriate materials and tools to solve a problem (e.g., countables, measurement tools, calculators).
  
• Use strategies (guess and check; act it out; make/use a list, chart; make/use a graph; build a model; draw a picture; use estimation; use a pattern) to solve one-step routine and nonroutine problems.
  
• Solve problems by working collaboratively with a partner; explain how/why the solution makes sense.
  
• Share and explain (verbalize/record/demonstrate) thinking about how the problem was solved.
  
• Acquire confidence in using mathematics meaningfully to solve problems.
  

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