Math: Grade 1

Draft Standards From The State of California Academic Standards Commission

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State of California Academic Standards Commission

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Mathematics is a language we use every day, often without knowing it. It builds and draws on conceptual understanding and skills, and helps us make decisions and solve problems. In this draft document we have tried to connect the notion of problem solving to conceptual understanding and skill development by embedding it within the content strands at every grade. Given here are only some of the ways you will see this exemplified. Students are asked to:

• ask relevant questions about problem situations
  
  
• decide between relevant and extraneous information
  
  
• choose appropriate operations tools and approaches to problem situations
  
  
• decide whether an exact or approximate answer is called for
  
  
• apply specific techniques in new situations
  
  
• explain, check, justify, prove, and judge the reasonableness of results
  
  
• create new approaches and connect knowledge and understanding in new ways
  
  

Number Sense

1. Students identify and represent the number and order of objects.

1.1 count, read, write, order, and compare (using words ... greater than, less than, equal to ... and symbols, <, >, = ) whole numbers to 100

1.2 identify ordinal positions first through tenth

1.3 locate, sequence, and represent whole numbers up to 10 on a number line

1.4 count by 2s, 5s, and 10s to 100 and count backwards from 100 by ones

1.5 identify the number of pennies equivalent to a nickel, a dime, and a quarter and find sums of money up to $1.00

2. Students demonstrate understanding of the base ten place value for two-digit numbers.

2.1 identify the place value of each digit in numbers to 100

2.2 use words, models (e.g., groups of objects), and expanded form (e.g., 24 means 20 + 4 or two bundles of 10 rods and 4 additional rods) to represent two-digit numbers

2.3 mentally identify one more than, one less than, ten more, ten less with numbers and sums up to 100

2.4 select a reasonable order of magnitude of one- and two-digit numbers to represent and describe problem situations

3. Students demonstrate the meaning of addition (putting together, increasing) and subtraction (taking away, comparing, adding on) and use these operations to solve problems.

3.1 estimate and find the sum or difference of two whole numbers (each 100 or less) or three one-digit numbers written in vertical and horizontal form

3.2 recall basic addition facts, sums to 18, and the corresponding subtraction facts

4. Students count concrete objects by grouping them (foundation for multiplication) and divide groups of objects into equal parts (foundation for division).

4.1 group objects by ones and tens

4.2 estimate the number of sets of a given size within a group of objects (e.g., make about four teams each with 5 members from the students in this class)

4.3 divide groups of objects into equal sets including groupings that create a remainder

Task/Assignment

Here are eight marbles. Give Mario half and you keep half. How many do you each get?

How many cookies would you need if each student in the class gets two cookies?

We have 42 cookies. How many can each student in class get? Will there be any left over?

Symbols and Algebra

1. Students select and use numbers, operations, and number sentences to describe problem situations.

1.1 use blanks, boxes or other symbols, and an appropriate operation to describe and solve simple situations involving addition and subtraction and interpret the results

1.2 write and solve number sentences that express relationships involving addition and subtraction including the correct interpretation and usage of the +, -, and = symbols

1.3 describe a problem situation that could lead to a given number sentence

Task/Assignment

There are three cats in the pet store window. Tommy buys one of them. How many cats are left in the window?

 ­ 3 = 8, 8 + 3 = , - 8 = 3 represent a set of related number sentences.

Measurement and Geometry

1. Students compare two objects according to weight, length, or capacity using direct comparison, non-standard units, and standard units.

1.1 compare the length/weight (using a balance) of two or more objects using a reference object or a non-standard unit

1.2 demonstrate understanding that measurement is accomplished by identifying a unit of measure, iterating that unit, and comparing it to the item to be measured

1.3 estimate and measure length and perimeter of an object using customary and metric units to the nearest inch and centimeter

1.4 order similar objects (e.g., from smallest to largest; longest to shortest, lightest to heaviest)

2. Students estimate and measure temperature and time using small basic units.

2.1 measure and tell time using analog and digital clocks to the nearest quarter hour, five minutes, and minute, and compare time related to events (e.g., before/after, shorter/longer)

2.2 estimate and measure temperatures at or above zero using Celsius (C°) and Fahrenheit (F°)

3. Students identify and describe the attributes and location of geometric objects and classify or sort the objects by these attributes.

3.1 identify faces of three-dimensional objects as triangles, rectangles, squares, or circles

3.2 identify geometric shapes that have bilateral symmetry

3.3 give and respond to directions, describe, and arrange objects in space in terms of proximity, position, and direction (near, far, below, above, up, down, behind, in front of, next to, left/right)

Task/Assignment

Which rocks are heavier than the block? Which are lighter? Which are the same weight?

Use pieces of spaghetti to measure the height of four students from different classes and name them in order from tallest to shortest.

Functions

1. Students sort objects, complete, and describe patterns involving numbers, shape, size, rhythm, or color.

1.1 describe, extend, and explain how to get to the next element in growing and repeating patterns, including rhythmic, numeric, color and shape patterns e.g., 3,5,7,9,...;

1.2 sort objects into an array based on two properties, describe, and extend patterns involving two attributes

Statistics, Data Analysis, and Probability

1. Students collect, read, interpret and compare data from simple graphs and prepare their own graphs.

1.1 gather, record, read, interpret, and compare data in bar graphs, tally charts, and picture graphs

1.2 compare data using the concepts of largest, smallest, most often, least often

Credits

The Draft Standards were prepared by:

The State of California Academic Standards Commission
The Commission for the Establishment of Academic Content and Performance Standards Comments may be addressed to The Commission