Developing
Mathematical Understanding
for
New York State
Test Preparation.
Grade 3
In 21 easy thirty minute Student Centered Lessons covering all PreMarch Grade 3 New York State Mathematics Standards.
(See here for the New York State Pre & Post Standards for Mathematics http://www.emsc.nysed.gov/38/gr3prepost.htm)
Test Preparation for GRADE 3 Mathematics
Week 1
Lesson 1: State Standard: 3N1, 3N2, 3N3
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 6,3 & 9 to put on my mailbox. What number could my house be? Choose 3 different numbers and try it again.
State Standards Practice:(25 min.)
Ask the students to write the first ten skip counting numbers for 25’s, 50’s and 100’s to 1000. Eg. 0 25 50 75 100 125…etc.
On completion ask students to write the word for each number for the 25 Skip Counting sequence. Eg. 0 Zero 25 Twenty Five 50 Fifty 75 Seventy Five 100 One Hundred 125… One Hundred Twenty Five…etc.
(After 15 min.) Select 5 numbers between 0 and 1000. 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 3 Mathematics
Week 1
Lesson 2: State Standard: 3N5
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 24.
State Standards Practice:(25 min.)
Ask the students for different ways to decompose 246 Eg. 200 + 46 200 + 20 + 20 + 6 100 + 100 + 46 50 + 50 + 100 + 20 + 20 + 3 + 3 …etc.
Ask students to write their own 3 digit number and decompose as many ways as they can.
Share students solutions. (5 min.)
Test Preparation for GRADE 3 Mathematics
Week 1
Lesson 3: State Standard: 3N7, 3N8, 3N9
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 two numbers together. What might the answer be? Try it again with different numbers.
State Standards Practice:(30 min. total)
Ask the students to write the 1x and 0x tables Eg. 1 x 1 = 1 1 x 2 = 2 1 x 3 = 3…etc.
And 0 x 1 = 0 0 x 2 = 0 0 x 3 = 0…etc.
Share students solutions. (5 min.) Ask why this makes sense? Why is zero groups of 5 equal to zero? (0 bags of 5 apples) Why is one group of any number always that number? (1 bag of 5 apples) Have students write written explanations (to check understanding).
Ask students to write the number sentence for “ I had 5 toys and found 3 more. How many do I have now?” 5 + 3 = 8 Ask students to write the number sentence for “ I had 3 toys and found 5 more. How many do I have now?” 3 + 5 = 8 Share by asking “ whats the difference? ”
Get the students to draw the picture and explain in writing “Whats the difference between “ I have 3 bags of 5 candies” and “I have 5 bags of 3 candies”? ” Share
Discuss, draw and explain why (2 + 3) + 4 (2 apples and 3 apples and then I get 4 more) is the same as 2 + (3 + 4) (2 apples and then I got 3 and 4 more)(Associative Property of Addition)
Test Preparation for GRADE 3 Mathematics
Week 1
Lesson 4: State Standard: 3N10, 3N11, 3N12, 3N13, 3N14
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 half of them are yellow. What does my handful of Jellybeans look like?
State Standards Practice:(30 min. total)
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 6 dots: ½, 2/2 1/3, 2/3, 3/3 1/6, 2/6, 3/6, 4/6, 5/6, 6/6. Share.
Test Preparation for GRADE 3 Mathematics
Week 1
Lesson 5: State Standard: 3N12
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:(30 min. total)
Ask students to draw 5 pizzas and cut each into different fractions and label. Eg. ½, ¾, 2/6, etc.
Share solutions.
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 3 Mathematics
Week 2
Lesson 1: State Standard: 3N16, 3N17
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)
Ms. Gonzalez says Odd numbers are better than Even numbers. Is she right? (There is no correct answer, we are looking for understanding of odd and even and why they may prefer one over another).
State Standards Practice:
Provide each student with their own 100’s Chart. Ask them to color in all the Even Numbers one color and all the Odd Numbers another color.
Get them to write what they found.
Quickly share some findings.
Ask students to choose any two even numbers and add them together. Share findings. (All students should have had an Even Answer)
Ask students to choose any two odd numbers and add them together. Share findings. (All students should have had an Even Answer)
Ask students to choose one even and one odd number and add them together. Share findings. (All students should have had an Odd Answer)
Have students summarize these findings in their own words. Share.
Test Preparation for GRADE 3 Mathematics
Week 2
Lesson 2: State Standard: 3N18
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)
Rank these problems from Hardest to Easiest: 104, 1004, 57+3, 9 + 2 + 18 – 10, 1,000 + 1,000, 14 + 26.
State Standards Practice:
Provide each student with their own 100’s Chart. Ask them to solve “I saw 18 monkeys and then I saw 9 more. How many did I see?” Share strategies. (Eg. Counting up 9 by 1’s, Counting up 10 and back 1)
Have students make up own number problem (self differentiating), Write and solve. Ask them to try and find another way to find the same answer.
Share problems and strategies.
Ask students to do another but using 3 digit numbers.
Discuss using Counting Up to find the solution to 100 – 96. (Beginning from 96. count 97, 98, 99, 100. 4 jumps, so it is 4) Have student sue Counting Up to find: 100 – 95 100 – 80 110 – 80 111 – 79 211 – 79 Have students do some of own and share.
Test Preparation for GRADE 3 Mathematics
Week 2
Lesson 3: State Standard: 3N19
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)
Start at any number and create a skip counting pattern. (Eg, 22, 27, 32, 37, 42, …)
State Standards Practice:
Skip count with the class by 3’s, 4’s and 5’s to 100 guiding on the class 100’s Chart. Provide each student with their own 100’s Chart. Ask them to color in all the skip counting numbers for 3’s onto their own chart. Then repeat for 4’s and 5’s. Discuss the patterns colored.
Play “BUZZ” with the class for 3’s, 4’s and 5’s. OR Have students Skip Count by 3’s (or 4’s or 5’s) with each successive student saying the next skip count number in turn. Students sit if they say a number ending in zero. Continue until one student is left standing. E.g., Student 1 says 4 Student 2 says 8 Student 3 says 12 Student 4 says 16 Student 5 says 20 and sits down Student 6 says 24 And so on.
Test Preparation for GRADE 3 Mathematics
Week 2
Lesson 4: State Standard: 3N20, 3N21
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)
Five animals are standing behind a fence. How many legs might you see? (Answers depend on number of 2 and 4 legged animals used)
State Standards Practice:
Ask the students to draw a picture to represent and solve 3 X 5. (Eg. 3x5 array, 5x3 array, 3 groups of 5, 5 groups of 3). Share representations.
Ask students to show as many ways to solve 4 x 7 as they can. Share.
Ask students to draw their own multiplication picture and explain what it represents. Share with class and ask class to say what each picture represents.
Test Preparation for GRADE 3 Mathematics
Week 2
Lesson 5: State Standard: 3N22, 3N23
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 answer to a division question is 2. What might the question be? Write it as a Number Sentence and as a Word Problem.
State Standards Practice:
Ask the students to draw pictures to represent and solve: “If the zoo keeper wants the same number of animals in each cage. Show all the ways how the Zoo Keeper could keep 12 monkeys.” (1 cage of 12, 2 of 6, 3 of 4, 4 of 3, 6 of 2, 12 of 1)
Share.
Ask students to work out how to do similar with 36 snakes. (1 cage of 36 snakes, 2x18, 3x12, 4x9, 6x6, 9x4, 12x3, 18x2, 36x1) (If 36 too difficult, use 24)
Share.
Test Preparation for GRADE 3 Mathematics
Week 3
Lesson 1: State Standard: 3N25, 3N26, 3N27
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 10 shops in a row. If you walk up and back 4 times without getting to either end, how many shops might you have passed? (Answers will vary. Look for correct explanations)
State Standards Practice:(20 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 27 + 72 = (30 + 70 = 100)
Share students solutions.
Students make up 5 of own and estimate solution. (2 addition, 2 subtraction, 1 multiplication)
Test Preparation for GRADE 3 Mathematics
Week 3
Lesson 2: State Standard: 3A1
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 JoJo is older than his Dog, but younger than his Cat, what could the ages of all three be?
State Standards Practice:(20 min.)
Which side of > is larger? Which side is smaller?
Put these numbers on the correct side: 36 and 12  >  22 and 23  >  Do 5 of own.
Share students solutions.
Do 5 for  < 
Use the following numbers to fill in the 6 blanks. Each number can only be used once. 2, 5, 5, 7, 9, 10.  >   <   = 
Share students solutions.
Students make up inequalities of own. Test Preparation for GRADE 3 Mathematics
Week 3
Lesson 3: State Standard: 3A2
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 found a coin on Monday, two coins on Tuesday, 3 on Wednesday, 4 on Thursday and 5 coins on Friday. How much money might I have found for the week? (Answers will vary depending on value of coins found)
State Standards Practice:(20 min.)
Using their own 100’s Chart, students complete the following patterns for the next twenty numbers. (Color each pattern in a different color)
2, 5, 8, …
3, 9, 15, …
99, 95, 91, …
Students make up some or own.
Share.
Test Preparation for GRADE 3 Mathematics
Week 3
Lesson 4: State Standard: 3G1
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 found 5 shapes under my bed. How many sides might I have altogether?
State Standards Practice:(20 min.)
Put the following on an Overhead or on the board or onto worksheets for the students.
Get them to match the shape with the name, (individually or in small groups), with one sentence on how they know. Share student solutions.
Circle, Triangle, Square, Rectangle, Trapezoid, Rhombus, Hexagon.
Draw a picture using more than one of each shape (use imagination) and label the shapes.
Share students work.
Test Preparation for GRADE 3 Mathematics
Week 3
Lesson 5: State Standard: 3G3
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)
JoJo said a Pyramid has five points, while his teacher said it has five sides. Who is correct and why? (Both are correct if you count the base as a side, otherwise only JoJo is correct. Can be argued both ways)
State Standards Practice:(20 min.)
Draw each of the following showing 3 sides. (Student would benefit from having these 3D shapes on their table to see).
Cube, Cylinder, Sphere, Prism, Cone.
Draw a picture using each of the above shapes and label.
Share students work.
Test Preparation for GRADE 3 Mathematics
Week 4
Lesson 1: State Standard: 3M1, 3M2, 3M3, 3M4, 3M5, 3M6, 3M10
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 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:(20 min.)
Measure Length & height (to ½ inch) 3M2 Mass (ounces and pounds) 3M3 Capacity (cups, pints, quarts & gallons) 3M4, 3M5, 3M6
Provide students with access to the following, preferably at least one set per group. l 12 inch ruler l Scales to measure ounces and pounds l Measuring cup set (cup, pint, quart, gallon) l Counters to use in measuring (bears, blocks, cubes, etc.)
Have students measure 2 differently shaped open containers that are similar in volume. Try to find one that is short but fat, the other tall but thin. Ask students to work out which is bigger. Have students measure length, height, mass and volume of each. Discuss findings. Which is bigger? Does bigger mean Heavier? Larger Volume? Taller? Wider? (Note there is no real correct answer to this. Have students engage in discussion)
Test Preparation for GRADE 3 Mathematics
Week 4
Lesson 2: State Standard: 3M8, 3M9
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 breakfast last Saturday 3½ hours after I woke up. What time might I have woken up and what time might I have had lunch?
State Standards Practice:(25 min.)
Draw an analogue clock onto a blank page. Draw your favorite time of day onto the clock. Explain why this is you favorite time of day. Write underneath the clock what this time looks like on a digital clock.
Write what time it is ½ an hour after your favorite time of day. Do the same for ¼ of an hour after, ½ hour before.
Share.
Test Preparation for GRADE 3 Mathematics
Week 4
Lesson 3: State Standard: 3S2, 3S3, 3S4, 3S5, 3S6, 3S7, 3S8
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 graph in the paper showed more people liked Blue M&M’s that green. What might this graph have looked like?
State Standards Practice:(25 min.)
Open a bag of M&M’s and record the number of each color onto a Tally Chart with the following headings.
Color Tally Total
Place onto an Overhead Projector making a pictograph of the colors. E.g., Blue ●●●●●●● Green ●● Yellow ●●●●● Etc.
Have students draw a Bar graph showing the colors from the bag.
Share.
Test Preparation for GRADE 3 Mathematics
Week 4
Lesson 4: State Standard: 3G3. 3G4
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 opened my toy box and saw a toy made up of a cylinder, a sphere and a prism. What might it have looked like?
State Standards Practice: (25 min.)
On the shelf in the shop was a number cube (dice), a cylinder of chips, a sphere of the world, a prism of chocolate and a cone with icecream. Draw what the shelf might have looked like and label.
Share findings.
Draw what the shelf would look like from above. What would it look like from below?
Share.
Week 4
Lesson 5: State Standard: 3G5
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)
Dad said my picture was symmetrical. What might it have looked like?
State Standards Practice: (25 min.) Using the alphabet below, how many lines of symmetry in your full name? (Hint. Look for vertical and horizontal lines). What word can you find with the most lines of symmetry?
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Test Preparation for GRADE 3 Mathematics
Week 5
Lesson 1: State Standard: 3M7
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 was given $1.11 change at the store. What might it have looked like?
State Standards Practice:(30 min.)
How many different ways can you make $1.00 ?
E.g., Q, Q, D, D, D, N, N, N, P, P, P, P, P.
Show as many as you can.
Choose two of you solutions and write in correct Dollar and Cents notation.
E.g., .25 + .25 + .10 + 10 +10 +.05 +.05 +.05 +.01 +.01 +.01 +.01 +.01 = $1.00
Share.
