Summer Math Packet - Montgomery County Public Schools

Summer Math Matrix

Students Entering 4th Grade

Dear Parents / Guardians,

June 2014

Get ready for you and your child to discover mathematics all around you this summer! Just like reading, regular math practice over the summer (understanding, computing, applying, reasoning and engaging in math) will help students to maintain and strengthen the mathematic skills learned throughout the school year.

On our school website ( ) we have posted our Suggested Summer Math Activities. In order to best meet your needs, we are providing two options: a traditional Summer Math Packet and a Math Matrix. The activities in both options are aligned to the Common Core Standards and MCPS Curriculum 2.0. The tasks are designed to highlight the importance of math in everyday life. Our goal is for students to have fun thinking and working collaboratively to communicate mathematical ideas during the summer break.

Students may choose to complete the Summer Math Packet or the Math Maxtix.

Option 1: Math Matrix Students completing the attached Math Matrix are expected to complete at least three activities under each category (measurement topic). Activities are intended to be open-ended and engaging. Students may be creative and make changes to the tasks and/or create their own. The reflection sheet, along with any available math activities, should be collected to showcase summer learning. Math Evidence of Summer Learning: Reflection Sheet

Option 2: Summer Math Packet Summer Math Packets are posted on our website. Information & directions are included in each packet Math Evidence of Summer Learning: Completed Summer Math Packet

Students who turn in their Math Evidence of Summer Learning (noted above) in addition to their Reading and Writing Assignments by August 29th will participate in a celebration in September.

Have a great summer, having fun while engaging in meaningful and relevant math activities with your child. We will see you in August! Sincerely,

Scott Curry Principal

Cool Math Books to Read:

The $1.00 Word Riddle Book by Marilyn Burns Fraction Fun by David Adler The Best of Times by Gregory Tang Pigs Will Be Pigs: Fun with Math and Money by Amy Axelrod Counting on Frank by Rod Clement A Grain of Rice by Helena Clare Pittman Sideways Arithmetic from Wayside School by Louis Sachar Divide and Ride by Stuart J. Murphy Lemonade for Sale by Stuart Murphy

Reading a math book is a great way to engage in math and reading at the same time!

Be sure to include the math books that you read on your summer reading log.

Engaging Math Websites ? The following sites provide free online math tasks. Please review each site and monitor your child's online sessions.

(click on Games All Games) (free use - approx. 15 minutes /daily)

Popular Math Games: Monopoly, Othello, Battleship, Connect Four, Mastermind, Mancala, Legos, K'Nex, Simon, Yahtzee, Checkers, Racko, 24, Sumoko, Chips... Let us know if you have other favorites that we can add to the list!

Math Facts: Students need to become fluent with their math facts. Fluent math students are flexible, efficient and accurate! Take time over the summer to practice your facts and explore strategies to help you really know your facts!

Flash cards are available on several of the websites listed above. The AplusMath website includes online practice with flash cards as well as a Flashcard Creator. You can also create your own flash cards using paper or index cards. XtraMath () is a popular math facts practice website. An adult will need to activate a free account to obtain student access information. Have fun and challenge yourself!

GSCES Math Matrix_Students Entering Grade 4

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Number and Operations in Base Ten Operations and Algebraic Thinking

Use a variety of place value strategies to compose numbers when adding 3-digit quantities. e.g. n = 274 +358.

Create two numbers over 100. While adding, explain how place value helps you determine whether to compose a 10 or 100.

Use multiple strategies to subtract 3 digit numbers found in a magazine or book. Analyze which strategy is most efficient to solve the problem.

Work collaboratively to identify 5 numbers that would round to 400. Discuss the strategies used to round the numbers.

Discuss and identify scenarios during meals when you can separate objects in equal groups or shares.

Create and solve two step word problems based on real life situations. e.g. Johnny drove 238 miles to an amusement park. Sarah drove 52 miles more than Johnny. Andrea drove 87 miles less than Sarah. How many miles did Andrea drive to the amusement park?

Solve and explain one- and two-step addition and subtraction word problems that represent scenarios in their everyday life.

Use tiles as square units to form rectangular figures and identify equations to find the area using the number of rows and columns.

Identify and write equations for real-life situations when things must be shared (divided) into equal groups.

Use flashcards, playing cards, dice, etc. to solve basic multiplication facts of 2, 5, 10, 0, and 1 by memory.

Play a hop-scotch game to practice skip counting strategies to find the products of given multiplication equations.

Example: To practice products of 5 --? write on the ground all products in order, then after given a multiplication equation, hop-scotch to the correct product while calling out each product along the way.

Write multiplication or division equations that match drawings or pictures found in magazines or newspapers. Think about and discuss the reasoning as to why the equation matches the drawing or picture.

GSCES Math Matrix_Students Entering Grade 4

Number and Operations (Fractions)

Identify a unit fraction within a whole object. Example: Look at a whole graham cracker. What is the unit fraction if it is broken into 4 equal pieces? Take a walk around the neighborhood and justify whether objects are split into equal or unequal parts. If an object does have an equal number of parts, identify the number of parts and the unit fraction.

Example: equal parts = window panes (6 panes makes 6 parts so the unit fraction is

); unequal parts = garden

Draw a number line from 0 to 1 on the ground using chalk, sidewalk paint, etc. and split each whole into an equal number of parts without labeling each part. As a friend or family member calls out a fraction (for

example, ), stand on the mark that represents the given fraction and explain how the fraction on the number line.

Use a ruler to measure three different sized straight edged magnets, crayons, or

envelopes to the nearest inch and inch. Then compare the lengths and explain how fractions helped to measure the objects.

Measurement and Data & Geometry

Set a goal to find a certain amount of quadrilateral shapes around the home to sort into the categories of rhombus, rectangles, and squares. Explain why some quadrilaterals can be sorted into multiple categories.

Discuss situations for when and why it would be important to measure area.

Find, measure, and compare examples of area in your home or around your community.

Example: Use square sticky notes to measure the area of various rectangular table tops or book surfaces.

Analyze and explain whether the area of a rectangular figure changes based on horizontal or vertical positioning using plane figures.

Locate rectangular plane figures at the grocery store and evaluate addition and multiplication equations to find the total area of the figure.

Map out of a room in your house on graph paper and explain how to partition the shape to find the area.

Work diligently to compare and order liquid volumes of various containers around the home (for example: milk jugs, coffee mugs, juice boxes, cups, etc.).

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Number and Operations in Base Ten

Collaborate with a friend or sibling to generate division equations that represent a scene outside a window or in a store.

Find and explain patterns in 2's, 5's, and 10's, 0's, 1's multiplication facts. Identify and explain patterns in a multiplication table. Use models to represent equal share situations.

Write division equations to represent equal share situations.

Website to support learning: _contents.htm

Operations and Algebraic Thinking

Locate objects found around the home (ex: shoes, socks, forks) to create models of multiplication and division equations with an unknown. Monitor and discuss how the model matches the given equation.

Example: Model 6 x f = 18 by seeing how many groups of 6 tennis balls make a total of 18 tennis balls.

Use flashcards, playing cards, dice, etc. to solve basic multiplication facts of 2, 5, 10, 0, 1, 4, 8, 9, 3, 6, and 7 by memory. Website to support learning: . html

Identify situations at home where multiplication or division are used and write an equation.

Example: How many outfits can be created with 2 shirts and 4 shorts? 2 x 4 = n

Create an expense goal, write and solve a word problem and number sentence with an unknown that represents the goal.

Example: Our family created a goal to buy a new refrigerator that costs $500. If we save $50 each week, how many weeks will we need to save to be able to buy the refrigerator? (50 x w = $500)

Number and Operations (Fractions)

Create a new and original fraction number line game.

Find examples of food that are divided into equal parts (pizza, chocolate bar, graham crackers, orange slices). Represent the item by drawing a bar model.

Example: If you have a pizza divided into eighths, draw a bar model that is also divided in eighths). Create and explain equivalent fractions using the bar model

(e.g.: of the bar model is equal to ).

Create two models of fractions with the same denominator using paper plates.

Example: Show on one plate and on the other. Explain how the fractions compare by using the math terms greater than, less than, or equal to.

Find two similar shaped objects that can be divided into halves (an orange and a plum

or a book and a box). Show with each object and compare the halves. Explain if they are the same or not. Repeat this activity with other fractions.

Measurement and Data & Geometry

Create a goal to complete a task in a given amount of time (for example: complete homework, clean a room, etc.). Record the start and finish time to reflect on if goal was achieved. Add ideas to the original plan in order to improve the process of achieving the goal.

Use an analog clock to tell the time of athome activities (for example: start of sports practice, dinnertime, bedtime, etc.).

Use the grams of a given product, such as jelly, to determine what the total mass would be for several containers. Example: If one jar of jelly is 150 grams, how many grams of jelly would 5 jars be? How many bottles of jelly would there be if there were 750 total grams.

Determine the area and perimeter of windows in the home. Illustrate and label findings to determine if any windows have the same perimeter and different areas or the same area and different perimeters.

Create a data table showing the color and amount of socks in a sock drawer. Show the data in a different way such as a pictograph or a bar graph. Evaluate whether or not the scale should change based on the type of graph used.

GSCES Math Matrix_Students Entering Grade 4

Multiplication Table

GSCES Math Matrix_Students Entering Grade 4

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