1.0  NUMBER AND

OPERATIONS

1.1.1  Understand numbers, ways of representing numbers, relationships among numbers, and number systems

2.1.3 Solve problems, compute fluently, and make reasonable estimates.

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.

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1.1.1a  Count by twos, fives, and tens to 100.

1.1.1b  Count a group of objects (up to 100) by ones.

1.1.1c  Count a group of objects up to 30 by twos, fives, and tens.

1.1.1d  Count forward or backward by one beginning with any number less than 100.

1.1.1e  Recognize place value to 99.

1.1.1f  Read and write numerals up to 100.

1.1.1g  Count by tens from any number using a hundred chart.

1.1.1h  Estimate the number objects in a group and explain the reasoning for the estimate.

1.1.1i  Use manipulatives to model whole numbers to 99 (e.g., base-ten blocks, sticks, straws).

1.1.1j  Identify odd and even whole numbers to 50.

1.1.1k  Model halves and fourths of a single object or figure.

1.1.1l  Model halves and fourths of a set of objects.

1.1.1m  Match the spoken, written, concrete, and pictorial representations of ½ and ¼.

1.1.1n  Recognize one whole as two halves or four fourths.

1.1.1o  Count the value of a set of coins  (penny, nickel, dime, quarter) up to fifty cents.

2.1.3a  Solve story problems involving numbers to 100.

2.1.3b  Check for the reasonableness of solutions.

2.1.3c  Use calculators in problem-solving situations.

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.

How do you count by twos (fives, tens) to 100?

How do you count objects? OR Count the number of objects and tell me how many you have.  OR How many objects do you have?

Count these cubes by two’s (fives, tens) to 30.

How do you count backwards from 98 (or any other number less than 100) by ones?  How do you count forward from 76 (or any other number less than 100) by ones?

How many tens and ones are in this numeral?  How can you write and read numerals to 99? What does the 0 mean in this number?

How would you read (write) this numeral? 

How would you count by 10’s from 14 to 100 using this hundred chart?

About how many _____ do you think I have?  Why do you think that is a good estimate?

How would you show me 64 with these base ten blocks?

What is this number?  Is it an odd or even number?

How can you show a half (or fourth) of this pizza (or other object or figure)? How does haring a pizza relate to fractions?

How can you show a half (or fourth) of this set of objects?

When I say ½ (1/4) can you write the fraction and show a picture (using the pizza drawing)?

How do you say the name of the shaded part (of the pizza)?  How many (halves or fourths) are there in the whole (pizza)? How can this whole pizza be divided into equal parts?

How would you count these coins to tell me how much money you have?

How can you use the cent sign to write these amounts? Is this amount of money less than (<) or equal to (=) this amount?

Following the SOLVE model, how would you solve this problem?  How do you know what the problem is asking you to do?  What problem solving strategies could you use?  What is the first step you should take? 

How do you know if your answer is reasonable?  How could you avoid making errors?

How would you use the calculator to help you solve this problem?  Would you use a calculator when you can do addition/subtraction in your head?

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?

[Incorporate problem solving throughout the year.]

Teacher models problem solving process using

Think Aloud.

SOLVE MODEL

S—How do you study the problem?

O—How do you organize the data (or facts)?

L—How do you line up a plan?  What action do you need to take?

V—How do you verify your plan with action?  How do you take the planned action?

E—How do you evaluate the solution?  How do you know if your answer is right?

Problem-solving strategies-

Draws a picture

Makes lists or tables

Uses pattern blocks, tiles or other manipulatives

Systematic guessing and checking

Acting it out

Uses patterns

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.

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.

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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.