1.0  NUMBER AND OPERATIONS

2.1.1  Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

2.0  ALGEBRA

2.2.1  Sort and classify objects by size, number, and other properties.

2.2.2  Represent and analyze patterns and functions.

2.2.3  Use concrete, pictorial, and verbal representations to develop an understanding of the language and symbols of mathematics.

2.2.4  Illustrate general properties of operations.

2.2.5  Analyze change in various contexts.

3.0  GEOMETRY

2.3.1  Analyze characteristics and properties of geometric shapes.

2.3.2  Specify locations and describe spatial relationships.

4.0  MEASUREMENT

2.4.1  Demonstrate understanding of units of measure and measurable attributes of objects.

2.4.2  Apply appropriate techniques and tools to determine measurements.

5.0  DATA ANALYSIS AND PROBABILITY

2.5.1  Develop, select, and use appropriate methods to collect, organize, display, and analyze data.

2.5.2  Apply the basic concepts of probability.

E

E

E

E

E

E

I

E

E

E

E

E

C

I

E

I

E

E

I

E

E

E

E

E

E

E

C

C

E

E

I

I

I

E

E(M)

E

E

E

I

E

E

E

E

I or E

I

E

C

E

E

E

C

I

E

2.1.1a  Count a set of objects to 100 using an efficient grouping strategy (e.g., two’s, threes, fives, or tens).

2.1.1b  Count forward and backward by one from any number less than 999.

2.1.1c  Read and write numerals to 999.

2.1.1d  Recognize place value to 999.

2.1.1e  Identify odd and even numbers to 100.

2.1.1f  Use concrete models or pictures to show whether a fraction is less than a half, more than a half, or equal to a half.

[up to 12ths]

2.1.2b  Use the number line to demonstrate addition and subtraction.

2.1.2c  Write and identify number sentences that describe situations involving addition and subtraction.

2.1.2d  Write related addition and subtraction sentences.

2.1.3d  Add and subtract efficiently and accurately with single-digit numbers.

Recall and apply basic addition facts (sums to 18).

2.1.3e  Use a variety of strategies to add and subtract two-digit numbers. [& 3 digit numbers with & without regrouping]

2.1.3f  Explain and justify solution strategies used in problem solving.

2.1.3g  Use estimation to justify the reasonableness of a computation.

2.2.1a  Sort objects by two or more attributes.

2.2.1b  Identify the rules by which objects or numbers have been sorted.

2.2.2a  Extend a growing pattern.

2.2.2b  Identify the unit of a three-part repeating pattern.

2.2.2c  Translate a repeating pattern from one medium to another (e.g., red-blue-blue to snap-clap-clap).

2.2.2d  Determine the output for a particular input given the one operation function rule (i.e., addition, subtraction).

2.2.3a  Interpret and solve open sentences that involve addition or subtraction.

2.2.3b  Use the language and symbols of mathematics appropriately to communicate mathematical thinking.

2.2.3c  Use manipulatives to demonstrate addition and subtraction sentences written symbolically involving numbers 0-20.

2.2.4a  Apply the commutative property of addition.

2.2.4b  Show that subtraction is not commutative.

2.2.4c  Apply the addition and subtraction properties of zero.

2.2.5a  Describe qualitative change (e.g., student growing taller).

2.2.5b  Describe quantitative change (e.g., student growing two inches in one year).

2.3.1a  Recognize, name, build, draw, and compare two- and three-dimensional geometric figures.

2.3.1b  Describe attributes and parts of two- and three-dimensional geometric figures.

2.3.1c  Recognize shapes that have line symmetry.

2.3.1d  Investigate and predict the results of putting together and taking apart two- and three-dimensional geometric figures.

2.3.2a  Illustrate flips, slides, and turns using concrete and pictorial materials.

2.4.1a  Compare and order objects according to length, capacity, and weight.

[Measure & estimate length using standard and nonstandard units.]

2.4.1b  Demonstrate understanding of the concepts of perimeter and area.

2.4.1c  Identify the measurable attributes of objects in the environment.

2.4.2a  Read and write time to the hour, half-hour, quarter-hour [& to 5 min.] (using analog and digital clocks).

2.4.2b  Relate days, dates, weeks, and months to a calendar.

2.4.2c  Explain the relationship between inches and feet.

2.4.2d  Measure length to the nearest centimeter, foot, half-inch, and inch.

2.4.2e  Use strategies to make estimates of length and time.

2.4.2f  Solve problems involving elapsed time in hour intervals.

2.4.2g  Measure and estimate weight and capacity using a variety of non-standard units.

2.4.2h  Find area and perimeter using non-standard units.

2.4.2i  Read thermometers with Fahrenheit and Celsius scales.

2.5.1a  Pose questions and gather data to answer the questions.

2.5.1b  Read, interpret, and create tables using tally marks.

2.5.1c  Create pictographs and bar graphs.

2.5.d  Read and interpret tables, bar graphs, and pictographs.

Introduce concepts of mode, median, & mean.

2.5.2a  Predict outcomes of events based on data gathered and displayed.

2.5.2b  Explain whether an event is likely or unlikely.

How could you count the objects (up to 100) a fast way? Can you think of any other ways to count them fast? Explain your thinking about the strategies.

How do you count forward (and backward) from  ____ (any number less than 999)?

How can you read and write numerals to 999?

Can you tell me how many hundreds, tens and ones are in this number?

Is this number odd or even?

Show me an odd number.

How can you tell if a number is odd or even?

Tell me what part of the pizza (or other object) you have.  Is it less than half, more than half, or equal to half?

How can you show me (using the number line) 2 + 3 (or 3 – 2)?

How could you write this problem as a number sentence?

How would you write 2 + 5 = 7 as a subtraction sentence?  How would you write 7 – 5 = 2 as an addition sentence?

What happens when you add (or subtract)?  Does the total get larger (or smaller)?

Using your manipulatives, how can you show equal rows of 5?  How could you say that as multiplication?  How does addition relate to multiplication?

What would be the best way to add/subtract these number facts?  What is the quickest way you can show me your number facts?  Show how fast and accurately you can add (or subtract) these numbers.  How can you improve your accuracy…your speed?

How can you add (or subtract) these numbers?  Show how quickly and accurately you can add (subtract).  Tell me how you did it.

How would you use the SOLVE steps to tell about your problem?

Tell me which strategy you used and why?

How do you know what to do when the problem says the answer is “about”?  (“close to” or “near”)  How could you use your estimation to know if your answer is “close to” or “near”?  How do you know if your estimation is reasonable?

How could you sort these objects by ______(attribute) and by ______ (another attribute)?

Why did you sort/group these objects this way?

How would you continue or extend this pattern? What is the rule for this pattern?

Can you show me the unit/group that makes the pattern?  How do you know?

How can you show this color pattern (red-blue-blue) as a snap and clap pattern?

What do you know about the answer to a problem with a +…with a -?

What would you need to know to solve this addition (subtraction) sentence?  What is missing?  How would you solve it?

How would you use your math language (words) to tell me about this problem?

How would you use ______ (manipulatives) to show me this number sentence?

Is 4+5 the same as 5+4?  How do you know?  Is the answer to 3+4+3 the same as 4+3+3?  Why?

Is 5-4 the same as 4-5?  How do you know?

What happens when you add or subtract 0 from another #?

What does a 0 mean in this number sentence?  (3+0=____ or 3-0=____)  How do you know?  How would you show me with manipulatives?

What happens to your height and weight in one year?  How does your knowledge change?  What kind of change happens?

What happens to your height/weight in one (two) months.  Can you tell me how your knowledge changes?  How do you know?  What measures can you use to prove this change?

How many sides (or angles) does this figure have?  Tell me the name of these shapes.  How do you know?  Can you build/draw these shapes?

What would you tell me about this geometric figure?

Which lines in this shape are the same?  Which lines in this shape are symmetrical (same)?

How do you know?

How can these shapes be put together (or taken apart) to form a new shape?  Tell me what shape (or design) they will make.  How can you describe the shape (or design) you’ve created?

What happens when you flip (or slide, or rotate ____degrees) this figure?  How does it change?  Explain how to make a simple figure on a geoboard or dot paper.  Can you flip the figure?

How would you order these objects from shortest to longest (smallest to largest; lightest to heaviest)?  Looking at these four objects, which is the ______? How do you know?

What is perimeter?  What is area?  How can you tell me the perimeter of this object?  How can you tell me the area?

(Using objects in the classroom, home, outdoors) what could be measured?  What tool would you use?  How would you explain your answer in measurement terms?

Looking at this clock, how would you tell me the time to the nearest hour?  Half-hour?  Quarter-hour?

What can you tell me about the calendar?  How many things does the calendar tell you?

Is a foot longer or shorter than an inch?  How many inches are in a foot?  Using your measuring tool, what is an inch?  What is a foot?

Can you show me how long this ______ is to the nearest _____?  What is the length of this _____?  Can you tell me in inches, in centimeters?

Tell me about how long this ____ is.  Tell me about how long it takes to _____ (eat lunch, etc.) Is that a reasonable estimate?  How do you know?

Can you tell me how many more hours it will be until lunch?  Until playtime?  (If we go to the zoo at 1:00 and leave at 4:00, how many hours did we spend at the zoo?)

How would you use your estimation skills to tell me about your friend’s weight?  If you did not have a scale, how would you estimate the weight?  What might you use other than a scale to measure weight?

If you did not have a measuring tool, how could you find the area and perimeter of this room?

Can you tell me the temperature on the thermometer in both Fahrenheit and Celsius?

What are some questions we could ask and collect data to get an answer?  Where would you find the data you need?

How would you tell what this table says?  Which category has more or less?  How can you create a table using tally marks that would display the data we have about our question?

How could you show your information with a picture graph?  With a bar graph?

Tell me what information is on the graph?  What does this graph tell you?   Use the graph to tell me if this statement is correct (or incorrect).  Why? (or why not?)

How could you study the graph and predict what might happen?  What do you think will happen based on this graph?  What are the results of this experiment?

How likely is it for (event) to happen?  Based on the results of the poll, is it likely or unlikely to happen?

To help students memorize & internalize--

Teacher guides them in using patterns to develop strategies to remember basic addition facts.

It is recommended that teachers teach and have students practice with and without regrouping together.

Teacher models the process of “Guess, then verify.”

Introduce concepts of division (process of sharing or dividing the number of equivalent subsets in a given set) and multiplication (process of repeated addition). T models, creates, and describes mult. situations in which equivalent sets of objects are joined; & division situations in which a set of objects is separated into equivalent sets.

[circle, square, triangle, rectangle, hexagons]

Teachers guide students in cutting shapes apart and describe new shapes.

Use attributes to describe how 2 shapes or solids are alike or different.