Mathematics

Mathematics, Science and Technology

Standard 1—Analysis, Inquiry, and Design

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers and develop solutions.

Alternate Level - Mathematical Analysis

Key ideas -

1. Symbolic representation is used to communicate mathematically.

Performance indicators -

Students:

use mathematics and symbolism to communicate in mathematics.

compare and describe quantities.

demonstrate knowledge of mathematical relationships.

relate mathematics to their immediate environment.

Sample tasks -

This is evident, for example, when students:

draw 5 apples and 5 oranges and compare the quantitative similarity.
set the table by counting out sets of 5 dishes, spoons, forks, knives, etc.
identify symbols associated with money.
express verbally, through gestures or with pictures or objects, the concept of more.
name and identify 3 basic geometric shapes (circle, square, triangle).
identify basic coins and bills.

Alternate Level - Scientific Inquiry

Key ideas -

1. The central purpose of scientific inquiry is to develop explanations of natural phenomena in a continuing, creative process.

Performance indicators -

Students:

learn to ask "why" questions to seek greater understanding concerning objects and events they have observed and heard about.

Sample tasks -

This is evident, for example, when students:

blow bubbles into the wind using a wand. With teacher assistance, talk about why the bubbles drift in certain directions.
observe a variety of objects that sink or float when placed in a container of water and with teacher assistance, discuss why the objects float or sink.
observe a helium balloon floating compared to an air-filled balloon which does not float. With teacher assistance, discuss why one balloon floated and the other did not.

Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers and develop solutions.

Alternate Level - Engineering Design

Key ideas -

1. Engineering design is a repetitive process involving modeling and optimization, finding the best solution within given constraints which is used to develop technological solutions to problems within given constraints.

Performance indicators -

Students:

activate devices.

recognize why an object or choice is not working properly.

recognize how a defective simple object or device might be fixed.

under supervision, manipulate components of a simple, malfunctioning device to improve its performance.

design a structure or environment (e.g., a neighborhood) using modeling materials such as LEGO Duplo blocks, model vehicles, model structures, etc.).

Sample tasks -

This is evident, for example, when students:

turn on light switch, television or adapted toys.
select from a group of familiar household appliances such as toasters, microwave ovens, and televisions, those devices which are not working properly.
recognize that a flashlight needs new batteries.
replace batteries in a toy.
reassemble a ball point pen.
install a tape cassette properly into a cassette player.
build a building from LEGO Duplo blocks, including doors and windows.
construct a model of their community using models of objects typically found in a neighborhood or by using a computer.
tell about a model they have constructed. Draw a picture showing its major components.

Standard 2—Information Systems

Students will access, generate, process and transfer information using appropriate technologies.

Alternate Level - Information Systems

Key ideas -

1. Information technology is used to retrieve, process, and communicate information and as a tool to enhance learning.

Performance indicators -

Students:

use a variety of equipment and software packages to enter, process, display and communicate information in different forms using text, pictures, and sound.

access needed information from media, electronic data bases and community resources.

use familiar communication systems to satisfy personal needs.

Sample tasks -

This is evident, for example, when students:

ask questions of local experts invited to the school to share their expertise and talk about their jobs.
use communication boards to convey information and ideas.
use a cash register with picture symbols to enter the food items purchased in a restaurant.
use touch pads, pointers or the keys of a computer to access a simple computer program.
gather information from newspaper or magazine pictures to complete a collage on topics such as nutritious foods, contemporary sports figures, etc.
use a tape or CD player to listen to music.
select appropriate channel on the television.
communicate why playing a radio too loudly disturbs people.
use a library to get information on topics such as animals, weather, cultures, etc.
use a computer to get information from the internet or a CD Rom.

Standard 3—Mathematics

Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real-world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry.

Alternate Level - Number and Numeration

Key ideas -

1. Students use number sense and numeration to communicate mathematically and use numbers in the development of concrete mathematical ideas.

Performance indicators -

Students:

use single digit whole numbers to identify locations, quantify groups of objects, and measure distances.

use concrete materials to model numbers and number relationships for whole numbers and simple fractions.

relate counting to grouping using manipulatives.

recognize the order of whole numbers up to 12 and commonly used simple fractions.

recognize coins and dollars and their value.

Sample tasks -

This is evident, for example, when students:

identify their house and phone number.
count out 4 apples into sets of 2 groups.
divide a sandwich in half or a pizza into eighths.
count out 5 pennies for a nickel.
count and package up to 12 cookies into a bag.

Alternate Level - Operations

Key ideas -

1. Students use mathematical operations to understand mathematics.

Performance indicators -

Students:

add and subtract whole numbers under 12 using manipulatives or a calculator.

Sample tasks -

This is evident, for example, when students:

use blocks to add 2 plus 2.
use a calculator to subtract 1 from 10.
count out 5 markers; give 2 to a friend and understand that 3 remain.
count out appropriate utensils to set the table for 4 people.
use calculator to add purchases made at the grocery store.

Alternate Level - Measurement

Key ideas -

1. Students use measurement in real-world situations.

Performance indicators -

Students:

use appropriate standard and nonstandard measurement tools in measurement activities.

understand the simple attributes of length, weight, volume, time, and temperature.

measure the length or volume of an object.

collect and display simple data.

Sample tasks -

This is evident, for example, when students, with teacher assistance:

measure with paper clips, finger width or blocks.
create a chart to display the results of a survey conducted among the classes in the school, or graph the amounts of survey responses by grade level.
measure ingredients for baking using a 1 cup measurer, tablespoon and teaspoon.
demonstrate an understanding of the function of a clock and read/comprehend digital time.
visit a grocery store and use a scale to weigh various quantities of fruit.
use a clock to follow a schedule by the hour for the day.
using a calendar, mark days completed and record weather and special events by using picture symbols.
tell time by the half hour and hour using a manipulative clock.

Alternate Level - Patterns/Functions

Key ideas -

1. Students use mathematical patterns in a real-world situation.

Performance indicators -

Students:

recognize and duplicate simple patterns.

use a variety of manipulative materials and technologies to explore patterns.

recognize simple patterns in nature, art, music, and literature.

Sample tasks -

This is evident, for example, when students:

draw leaves, simple wallpaper patterns, or picture sequences to illustrate recurring patterns.
use nuts, washers and bolts to duplicate and assemble a pattern.
use templates to organize sets of materials for an assembly line process.
listen to music or a story and repeat the common pattern in each (i.e., chorus of a song or phrase of a story).
sequence a group of pictures or events

Standard 4—Science

Students will understand and apply scientific concepts, principles and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.

Alternate Level - Physical Setting

Key ideas -

1. The Earth and celestial phenomena can be described by principles of relative motion and perspective.

Performance indicators -

Students:

recognize patterns of daily, monthly and seasonal changes in their environment.

Sample tasks -

This is evident, for example, when students with assistance:

conduct a long-term weather investigation, such as collecting weather data on rainfall.
use a chart to keep track of daily weather using picture symbols to denote sunny, rainy and cloudy days.
participate in seasonal activities related to the environment (plant a vegetable/flower garden, rake leaves, cut grass, shovel snow).

Key ideas -

2. Many of the phenomena that we observe on Earth involve interactions among components of air, water, and land.

Performance indicators -

Students:

observe the relationships among air, water, and land on Earth.

Sample tasks -

This is evident, for example when students:

observe a puddle of water outdoors after a rainstorm and discuss where the water came from and where it may go.
assemble rock and mineral collections based on characteristics such as color or texture.

Key ideas -

3. Matter is made up of particles whose properties determine the observable characteristics of matter and its reactivity.

Performance indicators -

Students:

observe and describe properties of materials using appropriate tools.

observe chemical and physical changes, including changes in states of matter.

Sample tasks -

This is evident, for example, when students:

compare the appearance of materials when seen with and without the aid of a magnifying glass.
investigate simple physical and chemical reactions and the chemistry of household products, e.g., freezing, melting, and evaporating; a comparison of new and rusty nails; the role of baking soda in cooking or materials before and after they are burned.
make flavored ice pops and observe the change from liquid to solid.

Key ideas -

4. Energy exists in many forms, and when these forms change energy is conserved.

Performance indicators -

Students:

observe a variety of forms of energy (e.g., heat, chemical, light) and the changes that occur in objects when they interact with those forms of energy.

Sample tasks -

This is evident, for example, when students:

investigate the difference between wearing black material versus white material in the sun.

Key ideas -

5. Energy and matter interact through forces that result in changes in motion.

Performance indicators -

Students:

investigate the use of common forces (pushes and pulls) on objects, such as those caused by gravity, magnetism, and mechanical forces.

Sample tasks -

This is evident, for example, when students:

use simple machines to perform tasks.
observe and describe how a automatic garage door opens and closes.

Students will understand and apply scientific concepts, principles and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science.

Alternate Level - The Living Environment

Key ideas -

1. Living things are both similar to and different from each other and nonliving things.

Performance indicators -

Students:

explore the characteristics of and differences between living and nonliving things.

identify simple life processes common to all living things.

Sample tasks -

This is evident, for example, when students:

compare two animals for similarities and differences (lion and cat).
grow a plant and observe its changes from seed to plant.

Key ideas -

2. Individual organisms and species change over time.

Performance indicators -

Students:

explore how living things change over their lifetime.

observe that differences within a species may give individuals an advantage in surviving.

Sample tasks -

This is evident, for example, when students:

observe and state the difference between a baby and an adult.
observe and discuss the colors of an insect that help it blend with its environment.

Key ideas -

3. The continuity of life is sustained through reproduction and development.

Performance indicators -

Students:

observe the major stages in the life cycles of selected plants and animals.

observe evidence of growth, repair, and maintenance, such as nails, hair and bone, and the healing of cuts and bruises.

Sample tasks -

This is evident, for example, when students:

grow bean plants or butterflies; describe stages of development.
trim finger nails and observe the growth of the nails over a month.

Key ideas -

4. Organisms maintain a dynamic equilibrium that sustains life.

Performance indicators -

Students:

identify a few basic life functions of common living specimens (guppy, mealworm, gerbil).

identify some survival behaviors of common living specimens.

participate in activities that help promote good health and growth in humans.

Sample tasks -

This is evident, for example, when students:

observe a single organism over a period of weeks and describe such life functions as moving, eating, resting, and eliminating.
give examples of good health practices (brushing teeth, showering, resting).

Key ideas -

5. Plants and animals depend on each other and their physical environment.

Performance indicators -

Students:

participate in activities that demonstrate how plants and animals, including humans, depend upon each other and the nonliving environment.

participate in activities that demonstrate the relationship of the sun as an energy source for living and nonliving cycles.

Sample tasks -

This is evident, for example, when students:

investigate how humans depend on their environment (neighborhood), by observing and discussing the interactions that occur in carrying out their everyday lives.
observe the effects of sunlight on growth for a plant or garden vegetable.

Key ideas -

6. Human decisions and activities have had a profound impact on the physical and living environment.

Performance indicators -

Students:

participate in activities which show how humans have changed their environment and the effects of those changes.

Sample tasks -

This is evident, for example, when students:

demonstrate recycling practices.

Standard 5--Technology

Students will apply technological knowledge and skills to design, construct, use and evaluate products and systems to satisfy human and environmental needs.

Alternate Level - Engineering Design

Key ideas -

Performance indicators -

Students:

?recognize that an object or choice is not working properly.

?communicate how a defective simple object or device might be fixed.

?under supervision, manipulate components of a simple, malfunctioning device to improve its performance.

?tell how the device or object has been improved.

?design a structure or environment (e.g., a neighborhood) using modeling materials such as LEGO Duplo blocks, model vehicles, model structures, etc.).

?describe the design in words or drawings.

Sample tasks -

This is evident, for example, when students:

?select from among a group of familiar household appliances such as toasters, microwave ovens, and televisions, those which are not working properly.
recognize that a flashlight needs new batteries.
replace batteries in a toy.
reassemble a ball point pen.
install a tape cassette properly into a cassette player.
explain how wheels added to a model car. improve its function.
build a building from LEGO Duplo blocks, including doors and windows.
construct a model of their community using models of objects typically found in a neighborhood.
tell about the model they have constructed. Draw a picture showing its major components.

Alternate Level - Tools, Resources, and Technological Processes

Key ideas -

1. Technological tools, materials and other resources should be selected on the basis of safety, cost, availability, appropriateness and environmental impact; technological processes change energy, information and material resources into more useful forms.

Performance indicators -

Students:

use a variety of materials and energy sources to construct things.

assemble components using a fastening process.

process materials into more useful forms.

understand the importance of safety and ease of use in selecting tools and resources for a specific purpose.

develop basic skills in the use of hand tools.

use simple manufacturing processes (e.g., assembly, multiple stages of production, quality control) to produce a product.

Sample tasks -

This is evident, for example, when students:

use materials, joining them with the use of adhesives and mechanical fasteners to assemble a box or toy.
develop skill with a variety of hand tools and use them to make or fix things.
select the appropriate hand tool to assemble a toy.
use the correct kitchen utensils, pans, adapted equipment and simple appliances, while cooking.
glue wooden pieces together to make a toy.
form clay into a desired shape.

Students will apply technological knowledge and skills to design, construct, use and evaluate products and systems to satisfy human and environmental needs.

Alternate Level - Computer Technology

Key ideas -

1. Computers, as tools for design, modeling, information processing, communication, and system control, have greatly increased human productivity and knowledge.

Performance indicators -

Students:

use the computer as a tool.

Sample tasks -

This is evident, for example, when students:

use a computer to communicate their ideas/thoughts.
use a computer-operated voice command to move a wheel chair or turn the lights on and off.

Alternate Level - Technological Systems

Key ideas -

1. Technological systems are designed to achieve specific results and produce outputs, such as products, structures, services, energy or other systems.

Performance indicators -

Students:

identify and operate familiar systems.

assemble simple systems.

This is evident, for example, when students:

name and use a microwave oven to reheat leftover food.
communicate how a telephone system is used.
using modeling materials such as building sticks/logs, assemble a merry-go-round.
connect a battery, switch, and light bulb.

Students will apply technological knowledge and skills to design, construct, use and evaluate products and systems to satisfy human and environmental needs.

Alternate Level - Impacts of Technology

Key ideas -

1. Technology can have positive and negative impacts on individuals, society and the environment. Humans have the capability and responsibility to constrain or promote technological development.

Performance indicators -

Students:

demonstrate that certain technologies have safety issues.

participate in the disposal of materials in a responsible way.

Sample tasks -

This is evident, for example, when students:

demonstrate how electrical devices are potential shock hazards (e.g., sticking metal object into a toaster).
place used plastic, glass and paper in appropriate recycling bins.

Alternate Level - Management of Technology

Key ideas -

1. Project management is essential to ensuring that technological endeavors are profitable and that products and systems are of high quality and built safely, on schedule and within budget.

Performance indicators -

Students:

work cooperatively with others on a joint task.

participate in planning an event or activity.

Sample tasks -

This is evident, for example, when students:

take part in a mass production to assemble an object such as a clock or ballpoint pen.
with adult supervision, help plan the materials, activities and food needed for an outing.

Standard 6--Interconnectedness: Common Themes

Students will understand the relationships and common themes that connect mathematics, science and technology and apply the themes to these and other areas of learning.

Alternate Level - Models

Key ideas -

1. Models are simplified representations of objects, structures or systems used in analysis, explanation, interpretation or design.

Performance indicators -

Students:

construct and operate models in order to discover attributes of the real thing.

discover that a model of something is different from the real thing but can be used to study the real thing.

use different types of models, such as graphs, sketches, diagrams, dioramas and maps, to represent various aspects of the real world.

Sample tasks -

This is evident, for example, when students:

compare toy cars with real automobiles in terms of size and function.
model structures with building blocks.
describe the limitations of model cars, planes, or houses compared to real cars, planes or houses.
use model vehicles or structures to illustrate how the real object functions.
use an area map to travel from one location in the neighborhood to another.

Alternate Level - Magnitude and Scale

Key ideas -

2. The grouping of magnitudes of size, time, frequency and pressures or other units of measurement into a series of relative order provides a useful way to deal with the immense range and the changes in scale that affect the behavior and design of systems.

Performance indicators -

Students:

provide examples of natural and manufactured things that belong to the same category yet have very different sizes, weights, ages, speeds and other measurements.

identify the biggest and the smallest values of a system when given information about its characteristics and behavior.

Sample tasks -

This is evident, for example, when students:

compare the weight of small and large animals (turtle vs. elephant).
compare the speed of bicycles, cars and planes.
collect and compare data related to the height of the students in their class, identifying the tallest and the shortest.

Students will understand the relationships and common themes that connect mathematics, science and technology and apply the themes to these and other areas of learning.

Alternate Level - Equilibrium and Stability

Key ideas -

1. Equilibrium is a state of stability due either to a lack of changes (static equilibrium) or a balance between opposing forces (dynamic equilibrium).

Performance indicators -

Students:

observe a balance and notice what happens when objects are placed on the balance.

record body temperature, etc.

Sample tasks -

This is evident, for example, when students:

place a paper cup on one side of a balance and a glass cup on the other side and observe the change.
record their body temperature in different weather conditions and observe that the temperature of a healthy human being stays almost constant even though the external temperature changes.