------ Math Curriculum Mapping ------

Correlation Grid: Key Ideas to Mathematical Activities

Key Ideas: Math Number & Modeling/ Measure- Uncer- Patterns &

Reasoning Numeration Operations Multiple Rep ment tainty Functions

Activities:

1. Tables X X X X

2a. Snowman X X X X

2b. Number Books X X X X

3a. Green Beans X X X X X

3b. Bean Bag Tally X X X X X

4. Sort/Classify X X X

5. Body Meas. X X X X

6. Weather Watch X X X X X

7. Creating Patterns X X X

1. Mathematical Reasoning

Students use mathematical reasoning to analyze mathematical situations, make conjectures, gather evidence and construct an argument.

Students

begin to see relationships, find connections and make generalizations and predictions.

develop awareness of the relationship of numbers.

begin to organize their thinking and develop reasoning strategies to solve problems.

Tasks:

Develop an awareness of the concepts, words and symbols related to numbers as used in daily living.

Explore environment to see relationships.

Proceed from concrete manipulation to pictorial and symbolic representation.

Ask how and why questions such as: How did you figure that out? Why do you think that is the answer? How did you get the number ____ ?

 

(Mathematical Reasoning continued)

&127; Activity - Problem

&127; What tables would you use?

1. Model many examples of exemplars with the whole class and/or in small groups.

2. Present the following problem to the students:

The teacher wants to set up the classroom so that 10 children can sit at tables. Some tables have space for 4 children. Some tables have space for 2 children. Some tables have space for 3 children.

3. Children will draw, label, and/or write about their solution of how many children will be placed at each table.

4. Have students present their solution to the others. Allow for discussion and sharing of ideas.

2. Number and Numeration

Students use number sense and numeration to develop an understanding of the multiple uses of numbers in the real world, the use of numbers to communicate mathematically, and the use of numbers in the development of mathematical ideas.

Students

begin to recognize the use of numbers in everyday life.

develop number sense and use of numbers by sorting and classifying, comparing and ordering, rote counting, using one-to-one correspondence, estimating, and using numbers in plays, songs and games.

develop awareness of relationships between numbers through exploration, numeration, problem solving and discussing solutions.

use ordinal numbers up to fifth.

Tasks

Explore, through counting, the cardinal numbers of a multitude of sets and collections of real objects, such as the number of boys and girls, cookies, blocks, pencils ...

Develop the idea that if two sets can be matched or put into one-to-one correspondence, then they have the same cardinal number.

Observe numerals in the environment such as room, house or phone number, their age, height or weight.

Identify number names orally through 10 with exposure of numbers through 100.

Use daily calendar and number line to show number order.

Develop number recognition and number sense through games such as Green Beans, Racing Dice and In the River.

Use number badges to match number sets.

Picture number line to get idea of sequence and progression.

Develop the concepts of first, last and middle.

Use ordinal number names from first through fifth.

Stress ordinal numbers when lining up children.

Match one-to-one such as children to chairs or cups to saucers.

Make list/book of places that we see numbers day to day.

 

 

&127; Activity - Problem

&127; A. Snowmen

Materials: Teacher drawn poster of three or more snowmen, decorated with various scarves, hats, buttons etc.; 9x12 labeled drawing paper, crayons, pencils

1. Present poster for discussion. Encourage use of numbers as descriptors. Discuss similarities and differences.

2. Students will make posters to show the number of buttons, hats, scarves, etc. Each child will tell about only one item but will include all three snowmen.

3. Provide each child with a drawing sheet. The sheets should be labeled according to the objective for that child. For example a child with limited counting skills might count the number of mouths or hats. One with more skill could count hands, boots or eyes. A student with higher counting skills could count fingers.

4. Students will draw, number and label and/or write about their problem according to their ability.

5. Each student should present and explain their work.

(Number and Numeration continued)

&127; B. Number books

Materials: 6 by 9 construction paper - various colors, toothpicks (flat), pattern blocks and pattern block colored paper pieces, small beans, bingo markers, craft feathers, tiles and tile papers, glue. Overhead projector with tiles, pattern blocks for the overhead.

1. Discuss the number to be represented in the book. (We’ll use number 7 for this example.) Using an overhead projector, show some designs using seven pieces and have them described. What does it look like? How many pieces are used? Are all the pieces the same? How many different ways can we describe the design using numbers?

2. Have each child make several designs using 7 pattern blocks in each design. Have them choose their favorite design and duplicate it on a 6 by 9 piece of colored paper using the pattern block paper pieces. They should then label it as they see it. 7: 3,4: 2+7: or 1+1+1+1+1+1+1 might be some of the possible labels. Save papers.

3. Another day follow the same procedure making several designs using seven toothpicks. This time they can glue the toothpicks used onto a sheet of 6 by 9 paper. This is best done by filling soda bottle caps with glue and having them dip the ends in the glue and placing them in their designs. Once again label with a number or even a number sequence.

4. Continue on other days with the other materials. Always do designs with the concrete objects first if actual material to be glued is representational (such as pattern block, tiles).

5. Attach each child’s papers together to make their individual number book.

From Mathematics Their Way, p. 219

3. Operations

Students use mathematical operations and relationships among them to understand mathematics.

Students

count object sets

match numerals with sets of objects to ten.

combine sets and name the amount.

develop awareness of counting on, counting back and skip counting.

 

Tasks

investigate various numerical problems that arise in school such as attendance and calendar activities.

Put two simple sets together to produce a new set of less than 10.

Explore the idea of one more through sets of objects and through a sequence of sets containing 1-10 objects.

Engage in numerous individual manipulative experience to perceive that the cardinal number of a set remains the same no matter how the elements are arranged.

Discuss and use the concepts of before, after, and between.

Integrate the comparison of sets and counting with other activities such as cooking, housekeeping, stories, songs, games and block building.

Use number badges (only 10, 9, 8, 7, ... more days) for counting back when nearing the 100th day of school or some other special event.

Use skip counting (5’s, 10’s) for daily counting of pennies, paper clips, straws, etc. as part of calendar activities.

Manipulate sets to show other ways of noting a numeral: a set of 5 can also be a set of 1 and a set of 4.

(Operations continued)

Compare materials in terms of more, less, and equal.

Play various games using dice and spinners for number combinations.

 

 

&127; Activity - Problem

&127; A. Green Beans

Materials: Green Beans, table to enter results. See sample below.

1. Enter results of each bean throw, into table.

2. Ask each child to predict the number of white given the number of green.

3. Hold up a table completed by a student. Cover "white" results, and ask child to indicate what the hidden, "white" results are.

* Green Beans can be bought from a catalog or hand made with Lima beans spray painted on one side.

(Operations continued)

&127; B. Bean Bag Tally

Materials: 5 to 10 bean bags, target (empty 2 lb. coffee can), tally sheet.

1. Target practice. Child throws bean bags into can. Every time a bean bag goes in, make a tally mark. Ask child to report score.

2. This time tally the traditional way, make four vertical marks. The fifth is a horizontal line. Circle the five marks. Ask child to report.

3. Child will circle the tally marks. Then do it again. Continue until child has at least three circles. Ask child to report the score.

4. This time child should be interrupted before circles are completed. Ask child to report score!

The first score would be eight (5+ 3). The second score would be eleven (5 + 5 + 1).

4. Modeling/Multiple Representation

Students use mathematical modeling/multiple representation to provide a means of presenting, interpreting, communicating and connecting mathematical information and relationships.

Students

sort objects by color, shape, size and other attributes.

observe and discuss their surroundings.

collect, count, organize and display objects and information in a setting which values multiple representation.

Tasks

Prepare for number concept development through sorting and classifying activities using concrete objects such as buttons, blocks and bottle caps.

Explore likenesses and differences (color, shape, size, ...)

Compare materials in terms of more, less, and the same amount or equal.

Use floor graph with concrete objects such as favorite fruit or toy.

Sort children according to various attributes, such as long or short sleeves, with or without buttons, color of hair, ...

Represent the number of days in school in various ways: straws, pennies, paper clips, number line and tally lines.

After the children have had lessons about the months of the year and have become somewhat familiar with their birthday months. Construct a Birthday graph. Across the bottom of the graph list the months. Over each month enter the name and day of the child’s birthday that occurs that month. This graph may remain up for the remainder of the year. Lessons dealing with the calendar, seasons, yearly cycles and children’s birthdays can focus on the graph.

Use valentine conversation hearts to graph by color.

Play 20 questions to develop attribute awareness.

(Modeling/Multiple Representation continued)

Use "treasure" boxes to sort objects in at least two ways.

Group objects according to one or more attribute:
1. weight: fruits, rocks, clay, liquids
2. texture - smooth to rough: rocks, fabrics, foils, shells
3. Function: school tools, kitchen utensils

 

&127; Activity - Problem

&127; Sorting and Classification Walk

This lesson could be started with the reading of The Shapes Game by Paul Rogers or Shapes, Shapes, Shapes by Tana Hoban.

Materials: paper and crayons, camera (optional)

1. Discuss the various attributes that have been used for sorting and classifying.

2. Decide which attribute will be the focus of the walk: straight lines, curved lines, squares, circles, things made of metal, things that move, things with numbers, sounds, ...

3. Children describe what they find and draw it on paper. When applicable, texture rubbings could be taken.

4. Papers are saved from each walk to make an attribute book.

5. As each page is added, compare to previous pages. How are they the same? Different?

From Mathematics Their Way, p. 72

5. Measurement

Students use measurement in both metric and English measure to provide a major link between abstract mathematics and the real world in order to describe and compare objects and data.

Students

compare objects

make simple measurements using non-standard units.

distinguish similarities and differences between objects and figures.

recognize and identify plane figures.

begin to develop a sense of time using calendar measurement (days, months, year).

Tasks

Compare length, height, width and depth of various objects.

Use terms such as longer than, taller than, smaller, as long as, ...

Explore various non-standard units of measure, such as blocks, links, feet.... for length and distance; buttons, marbles, bottle caps.... for weight; cupfuls, bowlfuls,.... for capacity; and faucet drips, pendulum swings,.... for time.

Arrange Cuissenaire rods according to size.

Explore the environment and note objects with geometric shapes.

Collect boxes, bricks and other three-dimensional shapes. Relate counting activities to geometric activities, such as finding out how many faces, edges, corners,.... a cereal box has.

Provide experience with weight and volume first in the hands and then on balance scales, using terms as heavier or lighter than.

Provide sand/water area for exploration of volume.

Use real money in store and calendar bank.

 

(Measurement continued)

Compare weather, food and temperature in general terms. For example:, "Today is warmer than yesterday."

Provide cooking experiences for liquid and dry measurement.

Use songs and stories to learn names of days and months.

 

&127; Activity - Problem

&127; Body Measurement

Materials: Unifix cubes, string or ribbon, recording sheet.

1. Each child makes a Unifix cube train as long as his/her arm, leg or whole body. This is accomplished much easier if they work in pairs.

2. Count and record the number of cubes in their train. For example, "My arm is ____ Unifix cubes long."

3. Compare lengths of Unifix cube trains.

4. Take Unifix cube train and measure a piece of string or ribbon the same length.

5. Use ribbon to find 4 other things in the room (or at home) that are the same length.

6. Draw pictures of them to record their answers. Share and compare answers.

6. Uncertainty

Students use ideas of uncertainty to illustrate that mathematics involves more than exactness when dealing with everyday situations.

Students

discuss the certainty or uncertainty of and distinguish between a guess and an estimate.

give relatively accurate numerical estimations of simple collection number objects.

use color spinners and dice games for decision making.

create preference graphs and discuss them.

Tasks

Practice estimating sizes, using phrases like about as long as, almost as long as, wider than....

Discuss the certainty and uncertainty of events, such as whether a beanbag will land on number 3, whether a dog will fly....

Participate in activities which involve anticipating outcomes, such as stacking blocks until the pile falls and then guessing at what height other piles will fall.

Use more/less spinners at the end of a game when able to compare amounts to choose winner.

Use the language of chance, such as more likely, less likely....

Make predictions of outcomes in literature.

Take a handful of small manipulatives and estimate how many they have.

Estimate amount of sand needed to fill a large container.

(Uncertainty continued)

&127; Activity - Problem

&127; Weather Watch and Weather Discussions

When it comes to uncertainty there are few things that we encounter daily that can be more useful than weather, in illustrating uncertain.

1. Discuss the weather on a regular basis. Asking questions such as: Will it be cloudy or sunny? Will it rain or snow? How much do you think we will get? How cold does it feel to you? What is the temperature? How close was your estimate?

2. Children could be asked to assess the reasonableness of their answers. If it is sunny can you reasonably expect rain? If it is cloudy and the temperature is 70 degrees Fahrenheit, do you think it may snow? If the month is January what kind of weather could you expect next week? What if it is June?

3. During some of these discussions the teacher could help the children differentiate between a guess and an estimate. A guess is a judgment without actual knowledge or enough facts. An estimate is a judgment based on some known facts and should be done after some careful consideration.

7. Patterns and Functions

Students use patterns and functions to develop mathematical power, appreciate the true beauty of mathematics and construct generalizations that describe patterns simply and efficiently.

Students

discover and reproduce patterns found in their own environment (physical, pictorial, symbolic and representational).

explain patterns using themselves and concrete objects.

create their own patterns using objects, pictorial and symbolic representation.

repeat and create their own acoustic patterns.

Tasks

Create their own pattern with pattern blocks and build a wall around themselves.

Extend given pattern block walls to several feet.

Tap, clap, slap and snap patterns.

Rename patterns such as A, A, B; bird, bird, cat; 1, 1, 2.

Use calendar pieces to show different patterns for each month.

Create pattern necklaces using beads or dyed macaroni.

Find patterns in clothing, objects in room, nature.

&127; Activity - Problem

&127; Creating Patterns

Pattern can be created in a variety of ways. After a pattern has been created (ex: Unifix), ask children to reproduce a similar pattern in any of the following ways: Piano, Blocks, Claps, Beads, Headbands, Tooth picks, Necklaces.

add

addition

after

amount

angle

as many as

at least

before

beginning

between

both

calendar

circle

coin

cold, colder

collection

column

compare

construct

corner

cube

diamond

different

digit

dime

double

end

equal

estimate

even

face

figure

first, second, etc.

graph

guess

half

heavy, heavier, heaviest

how many

include

inside

last

least

left over

less

less than

light, lighter, lightest

likely

long, longer, longest

manipulative

match

math

measure

measurement

member

middle

minus

money

more

more than

multiply

nickel

number

numeral

odd

one more

outside

oval

parallelogram

pattern

penny

plus

problem

quarter

rectangle

relationship

remainder

row

ruler

same

section

separate

shape

short, shorter, shortest

side

similar

small, smaller, smallest

solve

square

subtraction

sum

symbol

symmetrical

table

tall, taller, tallest

tally

times

total

triangle

warm, warmer

worth

wide, wider, widest

zero