Developing
Mathematical Understanding
for
New York State
Test Preparation.
Grade 5
In 29 easy thirty minute Student Centered Lessons covering all PreMarch Grade 5 New York State Mathematics Standards.
(See here for the New York State Pre & Post Standards for Mathematics http://www.emsc.nysed.gov/38/gr5prepost.htm)
Test Preparation for GRADE 5 Mathematics
Week 1
Lesson 1: State Standard: 5N1, 5N2, 5N3
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
I bought the numbers 1,6,3,2 & 9 to put on my mailbox. What number could my house be? Choose 5 different numbers and try it again.
State Standards Practice:(25 min.)
Ask the students to write the first 20 skip counting numbers for 25’s, 50’s, 100’s and 1,000’s beginning at 5,000 up to 10,000. Eg. 5,000 5,025 5,050 5,075 5,100 5,125…etc.
As each student completes ask to write the word for each number. Eg. 5,000 Five Thousand 5,025 Five Thousand Twenty Five 5,050 Five Thousand Fifty 5,075 Five Thousand Seventy Five 5,100 Five Thousand One Hundred 5,125 Five Thousand One Hundred Twenty Five…etc.
(After 15 min.) Select 5 numbers between 0 and 100,000. Put in order from smallest to largest. Write each number in word form. Eg. 5 27 99…etc. Five Twenty Seven Ninety Nine…etc.
Share students solutions. (5 min.)
Test Preparation for GRADE 5 Mathematics
Week 1
Lesson 2: State Standard: 5N3
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
Write down all you know about the number 1,234.
State Standards Practice:(25 min.)
Ask the students for five different ways to decompose 12,346. Eg. 10,000 + 1,000 + 200 + 46 5,000 + 5,000 + 500 + 500 + 200 + 20 + 20 + 6 1,000 + 9,000 + 300 + 300 + 300 + 100 + 100 + 100 + 46 1,000 + 2,000 + 3,000 + 4,000 + 500 + 300 + 200 + 50 + 50 + 100 + 20 + 20 + 3 + 3 …etc.
Ask students to write their own 5 digit number and decompose as many ways as they can.
Share students solutions. (5 min.)
Test Preparation for GRADE 5 Mathematics
Week 1
Lesson 3: State Standard: 5N4
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
Add five numbers together. What might the answer be? Try to get the same answer again with different numbers.
State Standards Practice:(25 min.)
Candies come in 3 sizes: Individually Bags of 10 Boxes of 100 Cases of 1,000.
Draw 5 different ways I can have 1,234 candies. Eg. 1 Case 2 Boxes 3 Bags 4 Individual Candies 0 Cases 12 Boxes 3 Bags 4 Individual Candies 0 Cases 12 Boxes 1 Bag 24 Individual Candies
Choose own 5 digit number and show ten different ways to make that number.
Share students solutions.
Test Preparation for GRADE 5 Mathematics
Week 1
Lesson 4: State Standard: 5N8, 5N9, 5N10
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
Put in order from smallest to largest, and write in Dollar and Cents notation. Dime, Nickel, Dollar, Penny, Quarter, 4 Dollars and 8 cents.
State Standards Practice: (25 min.) Have students write the following numbers into the table below:
0.6, 0.31, 0.213, ½, 1, 2.001
Put in order from smallest to largest:
 <  <  <  <  < 
Test Preparation for GRADE 5 Mathematics
Week 1
Lesson 5: State Standard: 4N7, 4N8, 4N9 (all PostMarch Grade 4)
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
I have a handful of Jellybeans. One third of them are yellow. What does my handful of Jellybeans look like?
State Standards Practice:(25 min.)
Ask the students to draw 6 dots. Ask students to split them into 2 groups and color in one group. Eg. ● ● ● ○ ○ ○ Ask the students what fraction have we colored and why? 3/6 or ½. Because we have 3 out of 6 or one out of two. Ask what the bottom number is representing in the diagram? (the # of groups) What about the top number? (The number of groups colored / selected)
Draw another 6 dots and split into 3 groups. Color in one group. Ask the students what fraction have we colored and why? 2/6 or 1/3. Because we have 2 out of 6 or one out of three. Again have them explain in terms of what the bottom number represents and the top number represents.
Draw another 6 dots and split into 3 groups. This time color in two groups. Ask the students what fraction have we colored this time and why? 4/6 or2/3. Because we have 4 out of 6 or two out of three. Again have them explain in terms of what the bottom number represents and the top number represents.
Get students to show each of the following with 12 dots: ½, 2/2 1/3, 2/3, 3/3 1/4., 2/4, ¾, 4/4 1/6, 2/6, 3/6, 4/6, 5/6, 6/6 1/12, 2/12, 3/12, 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 10/12, 11/12, 12/12 Which of these fractions represent the same amount? (Equivalent). Share. Test Preparation for GRADE 5 Mathematics
Week 2
Lesson 1: State Standard: 4N9 (PostMarch Grade 4), 5N4, 5N5
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
My Mom cuts my sandwich into equal pieces. Draw what my lunch might look like.
State Standards Practice:(25 min.)
Ask students to draw 5 pizzas and cut each into different fractions and label. Eg. ½, ¾, 2/6, etc.
Ask students to draw 5 pizzas and cut each into different fractions and label. Eg. ½, ¾, 2/6, etc.
Share solutions.
Show all the different ways you could share one pizza amongst three people. E.g., 1/3 + 1/3 + 1/3 1/6 + 2/6 + 3/6 1/2 + 1/6 + 1/3
Share solutions. Which ones are the same?
Discuss what the Numerator and Denominator mean. 1 Number of pieces selected 2 Total pieces or groups.
Get students to write own understandings of Numerator and Denominator with an example.
Have students draw a long straight twizler. Have them show how they could cut it in ½, 1/3, 2/3, ¼, 2/4, ¾. This is to aid understanding of fractions on a Number Line. Share.
Test Preparation for GRADE 5 Mathematics
Week 2
Lesson 2: State Standard: 5N5
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
I had a handful of jelly beans. 1/3 of them were black. Draw what my handful of Jelly Beans might look like.
State Standards Practice:(25 min.) Draw on an OH or board.
Ask student how to show ½ on one of the diagrams. Get students to explain.
Ask to show for 1/3 and why. Ask to show for 2/3 and why.
Who has the most chocolate, ½, 1/3 or 2/3? Have students explain.
Ask students to work out who has the most chocolate by drawing: ¼ or 1/3
½ or 5/12 7/12 or 3/6
Share.
Test Preparation for GRADE 5 Mathematics
Week 2
Lesson 3: State Standard: 4N10, 4N11, 4N12 (All PostMarch)
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
I pulled out of my pocket three coins. How much money could I have had?
State Standards Practice: (25 min.) Draw on an Overhead or board.
Ask if this represents $1.00, what would a ½ dollar look like?
Provide students with copies and have them show the following: Penny, Nickel, Dime, Quarter, 30 cents, 3 cents, 33 cents.
Share.
Have students do amounts of their own.
Test Preparation for GRADE 5 Mathematics
Week 2
Lesson 4: State Standard: 5N11
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
We shared 2 pizzas for dinner last night. I ate ½ a pizza, Mom ate ¼, Dad ate ½ and my sister ate 1/8. How much was left over?
State Standards Practice: (25 Min.) If EDM Fraction / Decimal / Percent Cards are available use with one set per small group. Or these could be written onto index cards for matching. If the EDM Fraction / Decimal / Percent Cards are available, have each group sort the Percentage cards in order from smallest to largest. Then have them match up a Decimal card with each one of the Percentage cards. Lastly, have them match up a Fraction card with each Percentage / Decimal pair. (I would provide students with a calculator to assist with some of the fractions, e.g., for 3/8 put 3 divided by 8 into the calculator to get 0.375)
Otherwise, write on board and ask students (in small groups) to write in order in a list down the page. 10%, 16.6%, 90%, 40%, 12.5%, 60%, 20%, 33.3%, 80%, 66.6%, 30%, 25%, 87.5%, 100%, 75%, 37.5%, 50%.
Then ask them to match all of the following Decimals to each one of the Percents. 0.7, 0.3, 0.125, 1.0, 0.60, 0.9, 0.66, 0.40, 0.75, 0.875, 0.10, 0.25, 0.80, 0.375, 0.5, 0.33, 0.20, 0.166
Then ask them to match up all of the following fractions with each of the pairs made (Percent and Decimal) 1/6, 7/8, 3/8, ¼, ¾, 2/2, 7/10, 4/5, 2/3, 1/5, 1/10, 1/3, 1/8, 2/3, 3/10, 9/10, 2/5, ½.
Share findings. Test Preparation for GRADE 5 Mathematics
Week 2
Lesson 5: State Standard: 4N11 (Grade 4 Post March) 4N12 (Grade 4 Post March)
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
I had 4 coins in my pocket. How much money could I have had?
State Standards Practice: (25 Min.) Pose the problem “I bought 6 things that cost less than $1:00 each. Each item cost a different amount.”
What could I have bought? How much could each have cost? Put in order from least expensive to most expensive. What might be my total cost?
Share. Test Preparation for GRADE 5 Mathematics
Week 3
Lesson 1: State Standard: 5N6, 5N7
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
If I was able to share one bag of Jelly Beans with 4 friends, how many friends could I share 4 bags with?
State Standards Practice: (25 Min.)
If 5 Mice = 1 Duck And 3 Ducks = 1 Lamb. 2 Lambs = 1 Pig. 4 Pigs = 1 Cow.
How many mice = 1 Cow? Show all your reasoning.
Have students share their different strategies. Test Preparation for GRADE 5 Mathematics
Week 3
Lesson 2: State Standard: 5N12
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
I want to share my candy evenly with 1, 2, 3, 4 or 6 friends at school today. How many candies could I take?
State Standards Practice: (25 Min.) Practice Skip Counting by 3’s, 4’s, 6’s, 9’s to 100. Assist by pointing to the 100’s chart.
Provide each student with own 100’s Chart. Have students color in the Skip Counting numbers for 3’s, 4’s, 5’s, 6’s, 7’s, 8’s, and 9’s each in a different color all on the same chart.
Share: Why are some numbers not colored? (Prime numbers, only factors are 1 and that number)
Why are some numbers colored more than once? (Many factors, divisible by many numbers)
Which number has the most factors?
Test Preparation for GRADE 5 Mathematics
Week 3
Lesson 3: State Standard: 5N13, 5N14, 5N15
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
My friend and I went shopping. I went into every 4^{th} shop. My friend went into every 7^{th} shop. Which shops did we both go into?
State Standards Practice: (25 min.) Lowest Common Multiple (LCM). On a hundreds chart have students color in the multiples of 5. On the same chart, have them color in the multiples of 6.
Which numbers are colored in twice?
Why?
What is the smallest number colored in twice?
This is called the Lowest Common Multiple (LCM).
Share students work.
Do for 6 and 9 to find their Lowest Common Multiple (LCM).
Greatest Common Factor (GCF). How can we write 36 as Repeated Addition or as a Multiplication? (Eg. 2+2+2…, 3+3+3…, 4+4+4…, 6+6+6…, 12+12+12, 18+18. Or 18x2, 12x3, 9x4, 6x6, 4x9, 3x12 ,2x18) Color these numbers onto a 100’s Chart.
Do the same for 20. What numbers are colored in twice? Why?
What is the largest number colored in twice? This is called the Greatest Common Factor (GCF).
Find the GCF for 15 and 18.
Share. Test Preparation for GRADE 5 Mathematics
Week 3
Lesson 4: State Standard: 4N19 (Post March)
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
At the zoo there were the same number of birds in seven different cages. Could there have been 50 birds in total? Draw a Picture, Show the Number Sentences and Explain in words.
State Standards Practice:(25 min.)
Maria said if you know 2 x 4 = 8, its easy to work out 20 x 40, explain.
Share students work.
How could you use this to help with 20 x 43? (20 x 40 = 800 and 20 x 3 = 60, so 800 and 60 is 860)
Use this method to work out 30 x 235. (30 x 200, 30 x 30 and 30 x 5, then put together)
Share 369 candies among 3 friends using similar strategies of partitioning. 3(00) / 3 = 1(00) 6(0) / 3 = 2(0) 9 / 3 = 3 so 100 and 20 and 3 is 123.
Share. Test Preparation for GRADE 5 Mathematics
Week 3
Lesson 5: State Standard: 4N23 (Post March) 5N19, 5N20, 5N21, 5N22, 5N25
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
I shared my bag of candies among 4 people. There were 23 candies in the bag. How might I have shared this?
State Standards Practice: (25 min.)
Show on this diagram ½.
Show on this diagram 1/3.
Use this information to show on the following 1/2 + 1/3.
Show what is left if I had 1/2 a block of chocolate and then ate 1/3 of the block.
Show 5/6 – 1/2.
Show 3 of your own.
Share. Test Preparation for GRADE 5 Mathematics
Week 4
Lesson 1: State Standard: 5N18
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
Destiny said you can work out how to share 20 candies with 4 friends by using Division and Multiplication. Is she right? Explain.
State Standards Practice: (25 min.)
Please ( ) Parentheses Excuse Exponent My Dear X / Multiplication Division (Left to Right) Aunt Sally +  Addition Subtraction (Left to Right)
Have a student explain how this works with the following
2 + 5 x ( 7 + 3 ) 1. 7 + 3 = 10 2. 5 x 10 = 50 3. 2 + 50 = 52
Have students work out
( 4 + 4 ) + 1 x 2 + 3 x 4 – 5 / 5
Do some of own.
Share. Test Preparation for GRADE 5 Mathematics
Week 4
Lesson 2: State Standard: 5N24, 5N26, 5N27
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
There are 20 shops in a row. If you walk up and back 5 times without getting to either end, how many shops might you have passed?
State Standards Practice: (25 min.)
I am walking uptown through Manhattan and need to go to the bathroom. I know there is a Starbucks at every 10^{th} corner. I.e. at 10^{th}, 20^{th}, 30^{th}, etc. As I am heading uptown, where would be the closest Starbucks if I am on 9^{th} Street? 18^{th}, 27^{th}, 36^{th}, 45^{th} (keep heading up as it is the same distance to 40^{th} and 50^{th}), 54^{th}, (now closer to go back), 63^{rd}, 72^{nd}, 81^{st}, 90^{th}?
Discuss solutions.
Explain how you would use this estimation strategy to estimate the answer to 127 + 262 = (130 + 260 = 100 + 200 + 30 + 60 = 300 + 60 = 360)
Share students solutions.
Estimate by rounding to the nearest Whole Number 1.9 + 3.2 = (2 + 3 = 5) 6.8 + 9.9 = (7 + 10 = 17)
Do five of own and share.
Students make up 5 of own and estimate solution. (2 addition, 2 subtraction, 1 multiplication)
Share. Test Preparation for GRADE 5 Mathematics
Week 4
Lesson 3: State Standard: 5A1
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
The car carrying truck has 12 wheels. It has to pay a toll of $5.00 for every wheel including the trucks and the cars it is carrying. How much toll might it need to pay? (Share solutions in the form of a table I.e., )
State Standards Practice:(25 min.)
What would the Toll be for carrying 10 cars? (12 + 40)= $52 If it could carry 100 cars, what would the toll be? (12 + 400) = $412
In the problem above , which part is always the same? (The truck wheels, 12)
Which part changes? (The car wheels)
We can write an Algebraic Expression for this problem:
The Toll is the number of Truck wheels plus the number of Car wheels
OR
T = 12 + C
In this problem 12 is a CONSTANT as it never changes, while C is a VARIABLE as it changes. T is the answer.
Continued …..
The zoo always has 5 workers.
How many people would be at the zoo if there was 1 visitor as well?
2 visitors? 3 visitors? 5 visitors?, 10 visitors?, 100 visitors?
Complete the table and write an expression. Label the Constant and the Variable. (People = 5 + Visitors)(Constant = 5, Variable = people)
Test Preparation for GRADE 5 Mathematics
Week 4
Lesson 4: State Standard: 5A6, 5A7, 5A8, 5G1
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
The Rabbit ate all the carrots around the edge of a rectangular garden. How many carrots might it have eaten?
State Standards Practice:(25 min.)
Draw a picture frame made out of 6 Popsicle Sticks. Draw another with double the height and double the length. How many Popsicle Sticks did you need this time? Draw another again doubling the height and length. How many popsicle Sticks did you use now?
Complete the table if you kept doubling each time:
Share:
Test Preparation for GRADE 5 Mathematics
Week 4
Lesson 5: State Standard: 5G2, 5G3, 5G6, 5G7, 5G8, 5G9, 5G10
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
Match up the words with their meanings: 1. Congruent A. 180. 2. Similar B. Same Shape and Size. 3. Equilateral C. 2 sides the same length. 4. Isosceles D. All sides different lengths. 5. Scalene E. Same Shape, different Size. 6. The degrees on a triangle F. All sides the same length.
State Standards Practice:(25 min.) Identify each triangle as Scalene, Isosceles or Equilateral.
Show which triangles are Similar and which are Congruent.
Fill in the length of the missing sides.
Write the missing angles so each triangle adds up to 180 Degrees. Test Preparation for GRADE 5 Mathematics
Week 5
Lesson 1: State Standard: 5G4, 5G5, 5G11 4G6, 4G8 (PostMarch)
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
Write all the words to do with Quadrilaterals you can think of.
State Standards Practice:(25 min.) Using two triangles, make the following quadrilaterals: a) Square b) Parallelogram c) Rhombus d) Trapezoid e) Rectangle
For each state what properties make it that shape. I.e., what makes the square a square?
Draw the lines of symmetry on each quadrilateral.
For each shape show which lines are Intersecting, Parallel and Perpendicular.
Show and Acute angle, Obtuse
angle, a Right angle and a Straight angle.
Week 5
Lesson 2: State Standard: 5M1, 5M2, 5M3, 5M4, 5M5, 5M9, 5M10, 5M11
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
My dog is taller and longer than my cat. My cat weighs more than my dog. My dog drinks more than my cat. Show how tall my dog and cat might be, how much they might weigh and how much they might drink.
State Standards Practice:(25 min.)
Have student working in groups, estimate then measure the height of each person in the group
Provide each group with inch rulers, cm rulers, yard sticks and meter sticks. Record all results.
Share strategies.
Test Preparation for GRADE 5 Mathematics
Week 5
Lesson 3: State Standard: 5M6, 5M8
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
Mom said I have to go to bed when the hands on the clock shows a Right Angle. What time could this be?
State Standards Practice:(25 min.) Knowing that a circle has 360 degrees, show how we could cut a clock into 2 pieces, and how many minutes this would be on each piece (60 / 2 = 30) and how many degrees this would be (360 / 2 = 180) Check each with a Protractor
Complete the table:
Share.
Test Preparation for GRADE 5 Mathematics
Week 5
Lesson 4: State Standard: 5S1, 5S2, 5S3, 5S4 4S2, 4S4 (PostMarch)
Open Response: (5 min.)(Give the problem and let the students try to figure it out writing their solutions onto paper. After a few min. share their solutions)
The average age for our family is 20. What might our ages be?
State Standards Practice:(25 min.) From the last few days newspapers, record what the minute time is for sunrise or sunset.
Put the results onto a line graph.
Make a prediction from the graph on what the sunrise or sunset will be a) tomorrow? b) in one weeks time?
What was the average sunrise or sunset time for the last few days? Explain how you worked this out.
Share.
