READINESS SKILLS

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SETS AND THEIR NUMBERS

M.1.1 The students will practice grouping objects in a set and identifying properties

(Mostly oral vocabulary at this stage – Observe student’s correct pronunciation of words as they are introduced. Watch for, and correct mispronunciations such as “nummer” for number and free for “three”. Number Set

Have students sort and group objects into sets. Use buttons, beans, toys, etc. Have them tell why the objects belong together. Challenge them to note similarities and differences.

Give oral directions: Find all the blocks that are green. Draw a set of balls.

Science- Take a walk around the school building. Find things that are blue… that are big…that can move…that are like a circle.

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NUMBER SENSE

M.1.2. The students will recognize number concepts through 10. M.1.3. The students will identify number symbols through 10. M.1.4. The students will be able to associate number with the corresponding amount of objects.

Number words through 10: Zero One Two Three Four Five Six Seven Eight Nine Ten

Tell how many: ‘‘‘‘ _____ 555 _____ * * * * * * ______

Give oral directions: Tom has three clubs. Show how many this is. §§§ Mary drew four hearts. ©©©©

Science: Discuss with children the nutritional value of fruits. Have them identify their favorite ones. Real Life Skills: Reading addresses, phone numbers, book pages, grade and room numbers.

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ONE TO ONE CORRESPONDENCE

M.1.5. The students will identify sets with one to one correspondence.

One-to-one matching One-to-one correspondence

Practice with physical models: Show three green blocks Have the students make a set with the same number.

I gave Tom, Mary and use a piece of cake. Show how many pieces I would need. (use models)

Real Life – When distributing papers/supplies identify items that have one-to-one correspondence with the number of students in the class. Show an item such as an egg carton with compartments. Practice filling to show one-to-one correspondence.

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COMPARING AND ORDERING SETS AND NUMBERS

M.1.6. The students will compare sets of numbers. M.1.7. The students will order numbers to 99. M.1.8. The students will understand, read and distinguish between equivalent and non-equivalent groups. M.1.9. The students will use the number line to compare numbers through 20.

Same Different Alike Equivalent Non-equivalent More Most Less Least Fewer Number line

Use concrete objects to explain concepts of more, less, etc. SSSSS mmm Have students use number lines to identify the position of designated numbers. 0 1 2 3 4 Three is between _____ and _____.

Using physical models, ask questions such as: Which row has more children? Which has the most? Use a number line as an aid in problem solving. Model its use on overhead or desktop number lines. Have students draw simple pictures showing: 1. Same-equivalent amounts 2. Different- non-equivalent Draw a lollipop for each child. There were more flowers than pots. Circle flowers to show this.

Mathematics: Computation, estimation, problem solving strategies Real life skills: Give examples of real life number lines: ruler, thermometer, sidewalk games. Make a real life number line with the students. Ask questions, “Are there more boys in front if Tim or in back of him?” Real life – Have the children organize the things in their pencil case. Doing this, they can see how many of each item they have and if the amount is the same or different. Study Skills: Organize desk. Identify number of items: Crayons, books……. Language Arts – The Very Hungry Caterpillar Science – Collecting rocks, sticks, leaves

NCTM Addenda Series, Grade 1 Book

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COUNTING

M.1.10 The students will be able to count orally by ones through 99. M.1.11 The students will be able to identify the number or numbers that come before, after or between the number or numbers in given sequence.

Count Numbers 1-99 Before After Between

Oral counting of numbers. 1,2,3… 99 Before After _____45____ _____13____ Between 35_______37 21_______23

Begin at different numbers. Count forward and backward. Identify missing numbers: 7,8, ____, 10, 11, ____, _____, 14 Write the number that comes just before 15. Write the number that comes between three and five.

Mathematics: Calendar dates, pennies, counting rods Physical Education: Counting games and exercises Music: Counting songs Literature: Nursery rhymes such as One, Two, Buckle my shoe… Following sequences in dot-to-dot books Real Life: Talk about numbers listed in an elevator. If one number were covered with tape, how would you know which floor you were on?

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NUMBER PATTERNS

M.1.12 The students will recognize simple number patterns of two, three and four.

Patterns

Using concrete objects such as blocks, linking cubes, have the students create patterns. Gradually develop in terms of numbers. 1,2,1,2,1, ____ 2,3,2,3,2, ____

Using 1” graph paper, have the students use stickers, crayons, etc. to make a pattern. Make patterns using rubber stamps. Make up a story about your pattern.

Real Life: Observe different necklaces to see the pattern of bead colors and shapes. Make bracelets of pony beads, macaroni, etc. Allow students to choose their own pattern. Talk about patterns students have seen at home – wall paper, floor tiles, etc.

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READING NUMBERS WRITING NUMERALS

M.1.13 The students will read the symbols for the numbers through 100. M.1.14 The students will write the numeral that relates to a group of objects through 100.

Numerals through 100 IMPORTANT - stress the correct formation of numerals. Refer to handwriting guides for correctness.

Review the symbol for each number. Give practice identifying the numeral with given sets of concrete objects. Present the number words through ten, associating each with the group it represents and with the corresponding numeral. 5 $ $ $ $ $ five

Model using oral instructions. Construct simple boxes with four sides showing the following for 0 – 100. 4 VV VV four ii ii

Handwriting – Teach the correct formation of numerals. Music – Counting songs such as “The Angel Band” Handwriting song to the tune of “Mulberry Bush” 1- From the top make one stroke down (3X) To make the numeral 1 2 – Curve around and out again 3- Half around and half around 4- Down, over and down again 5- Down, around and over the top 6- All the way down and around again 7- Dot, over and down again 8- All the way round and all the way round 9- All the way round and down again 10- From the top go all the way round Literature – Ten Bears in My Bed by Stanley Mack Anno’s Counting Book by Mitsumasa Anno Bears on Wheels by Stan and Janice Bernstein

Number dominoes

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NUMBER WORDS

M.1.15 The students will read and write the number words through ten.

One Two Three Four Five Six Seven Eight Nine Ten (Note the correct pronunciation of words.)

Have the students identify set of objects by using number word instead of numeral: ◉◉◉◉◉◉ six ▩▩▩▩▩ five

Teach number vocabulary. Have students practice reading word problems in which number words are used: Frances had four books. William gave her two more. How many books did Frances have then?

Language Arts: Vocabulary, writing, number books Cooperative learning: Have students do a “Scavenger Hunt” for number words in newspapers, magazines, etc. As a group, make a chart of words found.

Number word puzzles

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ORDINAL NUMBERS

M.1.16 The students will identify ordinal numbers through tenth. M.1.17 The students will be able to associate the ordinal with the position of related numbers on the number line.

First Second Third Fourth Fifth Sixth Seventh Eighth Ninth Tenth

☺☺☺☺ first second third fourth

Using concrete objects, have the students act out the problem. e.g. The second person in each row, stand. Move the fourth desk to the right.

Language Arts: Reading: Sequences, ordering events. Physical Ed.: Use physical movement to identify positional relationships. Real life skills: telling position in line, marching in parades, and winners of a race. Social Studies: Following directions Science: Watching and marking the growth of a plant from first through tenth stage.

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SKIP COUNTING

M.1.18 The students will be able to count orally by 2’s to 20. M.1.19 The students will be able to count orally by 10’s to 100. M.1.20 The students will be able to read and write to 100 by ones, fives, and tens.

Twos Fives Tens

Count by 2. Tell the missing numbers. 2,4,6,8,___,___,

Count by 2. Tell how many in all. u u u u u u 2,4,__,__, Bake cookies and arrange them in packs of two, five, or ten. Make bead necklaces grouping colors in twos, fives, or tens.

Real life: Pairs of shoes, socks, etc. Money—nickels, dimes

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RATIONAL COUNTING

M.1.21 Using manipulatives, the students will count from 0 through 19 and sequence objects in that order. M.1.22 The students will compare numbers of items that they have counted.

Numbers 0 –19 Order Fewest Most

Use counters to count out the number specified. Use familiar objects/items in the classroom to demonstrate learning.

Count the balloons. Put the groups in order from fewest to most.

Oral communication skills: Follow orally steps to come to a finish line or to completion of an independent project. Social Studies: Make a simple map of the neighborhood. Have the students count the number of blocks from one street to another. Model and count the number of houses on each block. Science: Count and compare the number of leaves on different branches. Real life: Make connections with counting done by the Count on CTW’s Sesame St.

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ODD-EVEN NUMBERS PLACE VALUE DECADE NAMES AND NUMERALS

M.1.23 The students will use concrete models to determine if numbers are odd or even. M.1.24 The students will identify and show groups of tens. M.1.25 Using manipulatives, the students will demonstrate groups of ten. M.1.26 The students will understand and be able to identify the number of tens and ones in a given number from 0 through 99. M.1.27 The students will recognize decade names and numerals through ninety.

Odd numbers Even numbers Group Tens Ones Place value chart Ten Twenty Thirty Forty Fifty Sixty Seventy Eighty Ninety

Form students into groups. Have them “Buddy Up”. Those with Buddies/ partners are examples of even. Those without are examples of odd. Have students group manipulatives into groups of ten. Identify the decade numeral for each group. Use a place value chart to name tens and units Tens Ones 4 0 4 1 4 2 Write the numeral. 2 tens 7 ones 1 ten 2 ones 4 tens 5 ones

Color 10. ∆∆∆∆∆∆∆∆∆ ∆∆∆∆∆∆∆∆∆ ∆∆∆∆∆∆∆∆∆ ◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊◊---Write how many. ☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺ Count by 10. Write the missing numbers: 10, 20, _____, 40, ___, 60, 70, ___, 90

Discuss use of odd/even numbers Religion – Show the students the groups of ten beads on a rosary. Math Connections – Number of pennies to equal a dime, number of dimes to make a dollar, number of dollar bills to equal a ten-dollar bill, etc. Art, Language Arts – Ask the children to draw a picture of their favorite outdoor activity. Tell them to include at least ten items in their drawing. Have them tell the class about their drawing/ have them make up a story about the drawing.

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COMPARING NUMBERS USE SYMBOLS TO SHOW NUMBER RELATIONS

M.1.28 The students will compare numbers greater than 0 and less than 100.

< Less than > Greater than = equal to more most fewer fewest

7 < 9 20 < 50 8 > 4 30 > 10

Tony has five books. Sara has two books. Pam has six books. Who has the most? Who has the fewest? Who has more than Sara?

Real life – Compare objects in the classroom: number of desks in each group, number of boys and girls in a group, number of crayons in a box, etc. Social Studies, Science – Compare the number of people, houses, animals, etc. in pictures used for these content areas.

Literature – Counting books. Point out the concept of “one more than”. Art – Have the students draw a picture of a fish with an open mouth. Use the greater than symbol for the mouth. Point out that more can fit on the widest side of the sign.

BASIC FACTS OF ADDITION AND SUBTRACTION

Refer to concepts of addition and subtraction as developed in the “OPERATIONS” strand of Guidelines. Number Sense Concepts are presented in connection with these lessons.

NUMBER LINE

The number line is used as a tool for comparing numbers and for the development of the addition and subtraction concepts. Refer to those concepts for further development.

WHOLE NUMBER OPERATIONS D I D I D

USE CONCRETE OBJECTS TO MODEL OPERATIONS OPERATIONS INTRODUCED AND DEVELOPED IN PROBLEM-SOLVING / REAL LIFE CONTEXT USE SYMBOLS FOR OPERATIONS

M.1.29 The students will understand addition as the joining of two separate groups. M.1.30 The students will develop understand of concepts through a problem-solving context. M.1.31 The students will understand the meaning of and will use symbols for the operations of addition and subtraction.

Add Addition Operation Plus Plus sign + Sum Addend Equals “Other names”

Use concrete objects to model addition sentences. Give practice in development of related vocabulary. 1 + 1 à 2 2 + 1 } 1 + 2 } 3 3 + 1 } 1 + 3 } 4 2 + 2 } Addition Sentences 2 + 1 = 3 2 + 2 = 4

Use six counters. Use the counters to tell an addition story. Then complete each number sentence. ____ + ____= ____ ____ + ____ = ___ ____ + ____ = ___

Literature – Counting Books Manipulatives - Dominoes Lima Beans Straws Computer – games Journals – Write a story or explain your number sentences to a partner.

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ADD SINGLE DIGIT NUMBERS ADDITION FACTS THROUGH EIGHTEEN

M.1.32 The students will be able to relate addition facts through eighteen. M.1.33 The students will be able to read, recognize and solve a vertically written number sentence.

Vertical “Standing Straight” Up and down

Facts of 3: 1 + 2 = 3 2 + 1 = 3 Facts of 4: 1 + 3 = 4 3 + 1 = 4 2 + 2 = 4 (Develop facts through ten.) Use concrete materials (such as computer tear off strips) to model. 3 + 2 = 5

Susan had six cupcakes. Show the different ways she could put them on two plates. (5 + 1, 4 + 2, 3 + 3) Trace pattern blocks and color to show 7 + 2 = Teach students to read vertical notation correctly. 3 Three +1 One Equals 4 Four Give practice translating addition sentences from horizontal to vertical notation

Real life – Grouping cookies, candy, cereal, toys Manipulatives – Abacus Beads Tiles Peg Boards Buttons Bingo Chips Have students look in advertising circulars for pictures of items showing different combinations of numbers.

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ADDITION OF THREE OR MORE ADDENDS ASSOCIATIVE PROPERTY OF ADDITION

M.1.34 The students will understand that we can only add two numbers at a time. M.1.35 The students will learn that when there are more than two addends, two of them must be grouped together.

Addend Group

˜˜˜ ˜ ˜˜ (3+1) + 2 = 6 4 + 2 = 6

Jamel got 4 books from Nan, 1 book from Mary and 2 books from Carol. How many books did he get?

Real Life – Use real life situations to draw problems. Mathematics – Apply problem-solving steps to word problems. Avoid giving the impression that if a problem has more than two numbers, addition should be used.

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COMMUTATIVE PROPERTY OF ADDITION

M.1.36 The students will explore the order property of addition. M.1.37 The students will use a number line to add numbers. They will understand that to add you move to the right on the number line.

Order Number line Right

3 + 1 = 4 1 + 3 = 4 Use dominoes to show order property.

Ask students to give examples in real life where the result of placing things together is the same regardless of the order in which it is done.

Real Life – group cookies, candies, etc. together Writing – Have the students write original word problems using order property.

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ADDITIVE PROPERTY OF 0

M.1.38 The students will understand that adding 0 to a number or adding a number to zero does not change the number. M.1.39 The students will understand that when a zero is subtracted from a number, the number is not changed.

Zero Change

4 + 0 = 4 0 + 4 = 4 6 – 0 = 0 4 – 0 = 4

If the lunchroom worker ordered 5 packages of napkins Monday but did not order any more, how many packages will he be receiving? Toby had 4 blue books. Shawn had no more than or no less than Toby. How many did Shawn have? (subtraction by comparison)

Language Arts – Nursery Rhymes: Old Mother Hubbard, Jack Sprat

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CONCEPT OF SUBTRACTION SUBTRACT SINGLE – DIGIT NUMBERS

M.1.40 The students will understand that subtraction is the operation in which groups are separated, compared or taken apart or in which a missing addend is found. M.1.41 The student will learn basic subtraction facts through 18. M.1.42 The students will use a number line to subtract. They will move to the left on the number line to subtract.

Subtract Subtraction Operation Minus Take away Compare Minus sign (-) Difference Number line Left

Other names for 1: 2 – 1 3 – 2 Other names for 2: 3 – 1 5 – 3 Other names for 3: 4 – 1 Subtraction Sentences: 3 – 2 = 1 4 – 2 = 2

(Take away) There are six birds in a tree. Two birds flew away. How many birds were left? (Comparison) Tom has nine baseball cards. Bill has 4 baseball cards. How many more does Tom have than Bill? (Subtraction) Jill has six dolls. One is a Barbie doll. How many are not Barbie dolls?

Money – Have the student practice giving change for a nickel or a dime. Literature – Alexander, Who Used to Be Rich Last Sunday by Judith Viorst Language Arts – Have the students write original word problems for given number sentences. Check to make sure the various concepts are being used. Manipulatives – Use computer strips to model number lines. (Missing Addend) Joan wants to make 5 cards to send. She has 2 done. How many more will she have to do?

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ADD MULTI-DIGIT NUMBERS- NO REGROUPING SUBTRACT MULTI-DIGIT NUMBERS- NO REGROUPING

M.1.43 The students will use a number line to subtract. They will move to the left on the number line to subtract. M.1.44 Students will subtract multi-digit numbers without regrouping.

Place values Ones Tens

32 + 11 44 - 22

PROBLEM I D I	SOLVING USE A PLAN FOR PROBLEM SOLVING Understand the question. Plan. Choose a correct strategy. Do. Solve. Check Answer statement	M.1.45 The students will read and identify the facts given and ask questions asking the problem. M.1.46 Students will select an appropriate strategy. M.1.47 The students will apply the chosen strategy to the problem. M.1.48 The students will formulate another method for doing the problem in order to confirm their answer. M.1.49 The students will write a short, complete sentence to answer the problem’s question.		Read Identify Problem Facts Question “Math shorthand” F à Facts ? à Question Number Sentence Operation Plus Minus Sum Difference Greater Fewer Equation Model Picture Equation Model Drawing Graph Option Words included in the problem. Asking sentence Telling sentence	Mary had 3 ٭. She got 1 more. How many flowers in all? 1) F à 3 ٭ F à 1 ٭ Q à How many ٭ in all? --------------------------------- 2) After strategies are taught, children might choose from the following Number Sentence Draw a picture Make a model All would be considered appropriate strategies. Be careful not to give the impression that every problem can be solved by writing an equation or using an operation. This is only one of many strategies for problem solving. 3) 3 + 1 = 4 /// + / = //// ٭٭٭ + ٭ = ٭٭٭٭ 4) ٭ Ө ∆ ¤ Students might also choose to check by using manipulatives, etc. Once they have identified the question, have the students formulate a fill-in- the–blank answer statement. There are _4_ flowers in all. (It is important that you require the students to answer using a sentence. Do not accept numerical answers only.	Problem solving can be applied to all areas of real life as well as other content areas of the curriculum. It is important to teach the students good order in setting up problems, as this will help them to avoid careless mistakes as they develop problem-solving skills. There are many rich sources for problems solving in children’s literature. Language Arts Explain that every problem is like an asking sentence that needs a telling sentence for its answer.
I	USE VOCABLUARY AS A CLUE	M.1.50 The students will use vocabulary as an aid in problem solving.			Refer to suggestions listed under “Vocabulary of Operations” in Operations strand. Give practice in de-boning problems.	Language Arts: using context clues in reading
I	USE PICTURES AND MAPS AS CLUES	M.1.51 The students will use pictures and maps as aids in problem solving.	Map		Make use of picture books/stories from children’s reading material to pose problems. Discuss how picture clues can help in solving problems. Have the students construct a neighborhood map with juice cartons, etc. Create original problems based on the map.	Social Studies: Maps Language Arts: Use picture clues and graphic aids in reading. Oral and written Language skills – create original problems cased on pictures, maps.

MODEL FOR PROBLEM SOLVING CHARTS

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USING GRAPHS, CHARTS AND TALES AS AIDS TO PROBLEM SOLVING USE CONCRETE OBJECTS TO MODEL A PROBLEM. ACTING OUT THE PROBLEM USING PROBLEM-SOLVING STRATEGIES Draw a picture Guess and Check SELECT AN OPERATION SOLVE PROBLEMS WITH MORE THAN ONE ANSWER USE LOGICAL REASONING SOLVE PROCESS PROBLEMS ADDITION- BASIC FACTS SUBTRACTION BASIC FACTS USE REASONING FOR EQUAL, GREATER THAN, AND LESS THAN USING COMPEN- SATION COUNTING BACK COUNTING UP USE A REFERENCE POINT OR BENCH-MARK ESTIMATE VISUALLY ESTIMATE SUMS AND DIFFER-ENCES ESTIMATE LENGTH ESTIMATE WEIGHT ESTIMATE CAPACITY ESTIMATE TIME PLANE FIGURES RECOG- NITION BY NAME IDENTIFY BY ENVIRON- MENT COMPARE DRAW SYMMETRY CLOSED/ OPEN FIGURES POSITION DIRECT- IONALITY GEOMETRIC PATTERNS GEOMETRIC SEQUENCES SOLID FIGURES RECOG- NITION COMPAR-ISON MEASURE- MENT SENSE NON- STANDARD UNITS STANDARD UNITS CUSTOMARY UNITS METRIC UNITS TIME CALENDAR MONEY FRACTIONS

M.1.52 The students will be able to interpret a bar graph and a pictograph; they will construct a graph to determine amounts. --------------- M.1.53 The students will be able to make tally marks in a table to show how many. M.1.54 The students will be able to use patterns to solve problems. They will be able to formulate their own pattern and recognize those given. M.1.55 The students will be able to solve a problem by acting it out. M.1.56 The students will be able to draw a picture or use objects to depict the word problem. M.1.57 The students will be able to use manipulatives to show or prove an estimated answer. M.1.58 The student will be able to decide whether to add or to subtract by listening to story problems. M.1.59 The students will solve problems with more than one answer. M.1.60 The students will be able to solve problems using logical reasoning. M.1.61 The students will solve problems using elapsed time. M.1.62 The students will solve problems that cannot be solved by using an equation. M.1.63 The students will be able to state orally the basic facts of addition and subtraction. M.1.64 The students will compare numbers using mental math skills. M.1.65 The students will learn that when adding and subtracting near tens, rounding the number to ten and compensating will make the task easier.