**Number and Number Sense Strand**

**Lauren Stevenson, Christiana Connolly, Paige Roberts, Morgan Jacobsen**

**Place Value**

1st Grade:

Group a collection of objects into tens and ones to develop a sense of place value

Identify the place value of each digit in a 2-digit number

2nd Grade:

Read, write and identify place value for each digit in a 3-digit number

Compare 2 numbers beteween 0 and 999 using symbols (>, <, =) and words

3rd Grade:

understand place value for six digit numbers

round numbers less than 9,999 to the nearest ten hundred, and thousands place

compare numbers 0-9,999 using (>,<, or =)

4th Grade:

understand place value through the millions

rounding is expressed through the millions and rounded to nearest thousande, ten thousand, and hundred thousand

compare whole numbers through millions using (>,<, or =)

5th Grade:

round whole numbers to the nearest tenth, hundredth, and thousandths place

**Fractions, Decimals, and Ratios**

Kindergarten:

Recognize fractions as equal to parts of a whole, identifying one half and one fourth

Counting & Grouping

Kindergarten

Count forward to 100 and backwards from 10

Grouping objects to skip count by 5s and 10s to 100 and searching for patterns

Count orally, write, identify, and construct with objects numerals 1-15

Overview

Counting is a math concept and that can begin before children even reach school. Counting is more thoroughly developed in kindergarten, counting up to 100 and backwards from 10. Grouping is introduced when kindergarteners begin skip counting with manipulatives. Skip counting in kindergarten is introduced by 5s and 10s up to 100 and progresses through 1st and 2nd grade, with more numbers to skip count by, and even skip counting backwards by 10s from 100. Grouping also continues throughout math development and becomes an abstract thought later in addition. Counting is an important one because counting lays the foundation for addition, subtraction, and skip counting and skip counting lays the foundation for numeric patterns, relationships, multiplication and place value. Counting and grouping are basic foundations that are essential to the rest of mathematics.

Overview

This portion starts out as students recognizing fractions as a whole and parts (halves and fourths) that make up a whole. That later moves into understanding of halves, fourths, AND thirds while also having to write the fraction. In second grade the students begin looking at more parts (eighths, sixths, etc.) and comparing fractions.

The next focus is on incorporating models into the learning of fractions. Students should be able to write a fraction from a model and make a model from a fraction. Mixed numbers, decimals, and rounding are introduced in fourth grade. It then moves on to solidifying all other facts learned previously and putting that to use while the students compare and order fractions and decimals. Lastly, in sixth grade, ratios and percentages are introduced so students will be able to compare and order fractions, decimals, ratios, and percentages. They also start multiplying and dividing fractions in this grade!

Relationships & Properties

Literature Review

1. Leaping Lizards by Stuart Murphy (Kindergarten)

2. More or Less by Stuart J. Murphy (2nd grade)

3. Slugger's Car Wash by Stuart J. Murphy (4th grade)

4. Fractions, Decimals, and Percents by David Adler and Edward Miller (6th grade)

More or Less

By: Stuart J. Murphy

Grade:

2nd

SOLs:

2.1c-Compare two whole numbers using greater than, less than or equal to

2.4c-Recognize even and odd numbers

Leaping Lizards

Grade:

Kindergarten

SOLs:

K.4 The student will count by fives and tens

Review:

The book begins with a show about to start, yet the lizards aren't there. They begin to arrive in groups of 5 and groups of 10, with the total amount of lizards being 50. We could use this book to introduce skip counting and grouping; students could use concrete manipulatives to account for the group of lizards in 5s and 10s, and use the groups to skip count. Its great to get the students thinking about couting by more than one and how its quicker

Kindergarten

Compare or construct, and describe two sets of 10 concrete objects using terms more, fewer, or the same

Identify one more than and one less than a number

Describing positions using ordinal numbers (1st - 10th)

2nd Grade:

Identify and write ordinal numbers for 1st through 12th

Compare units of fractions

Recognize even and odd numbers

3rd Grade

Students use the inverse relationships between adding/subtracting and multiplying/dividing to solve problems

5th Grade:

characteristics of prime and composite numbers

characteristics of odd and even numbers

6th Grade:

compare data using ratios

identify and represent, and order and compare integers

describe absolute value of integers

positive exponents and perfect squares

**Websites**

Kindergarten- This website has many math games, however this one specifically works with using concrete objects to count. It tells you how many you need and you have to click on the objects until you reach the correct amount. Its nice because its immediately rewarding and it keeps going with bigger numbers.

http://more2.starfall.com/m/math-k/feed-animal/

load.htm?f&d=demo

Kindergarten - I thought this would be great to help students continue development of skip counting. It has a number line with some numbers missing, however you can tell what its skip counting by and you have to fill in the missing spots

http://www.mathsisfun.com/numbers/fill-missing.php?g=10s100&name=Skip%20Counting%20by%2010s%20to%20100

1st Grade -

This website is focused on a large range of skills and could apply to several different strands. However, there are several sections relating directly to the "Number and Number Sense" strand such as counting and fractions.

www.ixl.com

2nd Grade - This website contains vairous activities and game addressing a wide range of topics from place value to identifying even/odd numbers. There's a designated section with all of the topics relating to number sense.

www.adaptedmind.com

2nd Grade-

www.funbrain.com

3rd Grade - This website has multiplication/division/subtraction/addition games which would help in third grade because third grade focuses on relationships between those operations

3rd Grade - www.freemathhelp.com

http://www.multiplication.com/games/play/cave-run-multiplication

4th Grade - This website has the Core Curriculum standards attached to it to sift through the games that way which is helpful for teachers. I chose the decimal section for fourth grade so they can practice their decimals! But there are also other sections for other grades!

http://www.mathnook.com/math/skill/decimalgames.php

5th Grade - This website has games for all levels of math. Students can choose games based on a variety of mathematical concepts, such as fractions, geometry, ratios.

http://www.mathplayground.com/puzzle_pics_2/tilesmath_fractions.htm

6th Grade - This website provides games to help students practice math skills such as operations, geometry, and math facts.

http://www.coolmath4kids.com/

1st Grade:

Identify parts of a region/set that represent fractions for halves, thirds and fourths and write the fraction

2nd Grade:

Identify the parts of a set/region that represent fractions for halves, thirds, fourths, sixths, eighths and tenths

Write the fractions

Compare the unit fractions for halves, thirds, fourths, eighths and tenths

3rd Grade:

understanding fractions from a model (fraction boxes/picture representations)

being able to turn a fration into a model (including mixed numbers)

4th Grade:

order fractions in mixed number form (including equivalent fractions)

know what the "division" line is in a fraction

Identify decimals through the thousandths

Rounding decimals to nearest whole number, tenth, and hundredth

Writing the decimal and fraction equilvalent for a model

5th Grade:

round decimals to the nearest whole number, tenth, and hundredth

recognize fractions in their decimal form and vice versa

compare and order fractions and decimals

6th Grade:

describe fractions, decimals, and percents as ratios

identify fractions, decimals, and percents from representations

equivalent relationships among fractions, decimals, and percents

compare and order fractions, decimals, and percents

multiple representations of multiplication and division of fractions

Beginning in first grade, students start establishing place value through practices such as grouping collections into tens and ones. They also begin identifying place value for 2-digit numbers-this is the first step in progressively identifying a greater number of place values. In 2nd grade, they identify for 3-digit numbers, in 3rd grade for 6 digit numbers and in 4th grade, they will identify place value through the millions. Rounding is also an integral part of the place value piece and starts appearing in 3rd grade. Additionally, comparison of numbers-using terminology such as greater than, less than and equal to-is paramount to place value concepts. This starts appearing in 2nd grade utilizing numbers between 0 and 999 and consistently appears in SOLs through 4th grade, when the students use numbers through the millions.

Overview

Slugger's Car Wash

by Stuart J. Murphy

Grade:

Sol's:

Review:

4th

4.3 (a): read, write, represent, and identify decimals expressed through thousandths; and SOL 4.3(b) round to decimals to the nearest whole number, tenth, and hundredth

The kids in the book are trying to raise money fast. CJ has to make change from different money amounts. We could use this to introduce decimals and how they are connected with our base-10 number system. The students could keep track of the money by first estimating and rounding and then figuring out the exact amount

Grade:

6

SOL:

6.2-The student will b) identify a given fraction, decimal, or percent from a representation and c) demonstrate equivalent relationships among fractions, decimals, and percents

Fractions, Decimals, and Percents

Review:

This book explains how children use fractions, decimals, and percents to play games at a fair. It focuses on explaining how these concepts represent parts of a whole. This book provides a relatable way for students to understand the relationship among fractions, decimals, and percents in real life situations.

1st Grade

Count from 0 to 100 and write the corresponding number

Group a collection of up to 100 objects

Count forward by 1s, 2s, 5s and 10s to 100 and count backwards by 1s from 30

2nd Grade

Skip count by 2s, 5s and 10s to 100 starting at various points

Count backwards by 10s from 100

Determine patterns created by counting by 2s, 5s & 10s on the hundreds chart

Overview

In Kindergarten, students learn how to compare concrete sets of objects using terms such as more than, fewer than, and the same as. They also describe positions using ordinal numbers up to the 10th place. In second grade, students progress to learning and identifying ordinal numbers up to 12th. Students also start to learn about fractions, and compare the sizes that fractions represent. The principles of even and odd numbers are explored in second grade as well. When students are in fifth grade, they continue to learn about even and odd numbers, and are introduced to the characteristics of prime and composite numbers. This allows them to explore the relationships between numbers and operations of numbers. During sixth grade, students learn about ratios, and they compare data using ratios. They also identify, order, and compare integers and describe the absolute value of integers. Students progress from learning about numbers to understanding how numbers relate to each other and share certain properties.

By: Stuart J. Murphy

Review:

This book involves a young boy named Eddie who has to guess people's ages by asking questions involving 'more' or 'less.' If he incorrectly guesses the age, he'll get dunked. Can he stay dry? This book tests students' ability to compare numbers using >, < or =.

by David Adler and Edward Miller