Developing
Mathematical Understanding
for
New York State
Test Preparation.
Grade 4
In 24 easy thirty minute Student Centered Lessons covering PreMarch Grade 4 New York State Mathematics Standards.
(See here for the New York State Pre & Post Standards for Mathematics http://www.emsc.nysed.gov/38/gr4prepost.htm)
Test Preparation for GRADE 4 Mathematics
Week 1
Lesson 1: State Standard: 4N1, 4N2, 4N3
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 & 9 to put on my mailbox. What number could my house be?
State Standards Practice:(25 min.)
Ask the students to write the the first 20 skip counting numbers for 25’s, 50’s, 100’s and 1000’s beginning at zero up to 10,000. Eg. 0 25 50 75 100 125…etc.
As each student completes ask to write the word for each number. 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 10,000. 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.
Test Preparation for GRADE 4 Mathematics
Week 1
Lesson 2: State Standard: 4N5
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 124.
State Standards Practice:(25 min.)
Ask the students for different ways to decompose 1,246 Eg. 1,000 + 200 + 46 500 + 500 + 200 + 20 + 20 + 6 300 + 300 + 300 + 100 + 100 + 100 + 46 500 + 300 + 200 + 50 + 50 + 100 + 20 + 20 + 3 + 3 …etc.
Ask students to write their own 4 digit number and decompose as many ways as they can.
Share students solutions.
Test Preparation for GRADE 4 Mathematics
Week 1
Lesson 3: State Standard: 4N4
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 three different numbers together to make a total of 120. Try to get the same total again with a different three numbers.
State Standards Practice:(25 min.)
Candies come in 3 sizes: Individually Bags of 10 Boxes of 100.
Show 5 different ways I can have 234 candies.
E.g. 2 boxes 3 bags 4 individual candies 0 boxes 23 bags 4 individual candies 1 box 12 bags 14 individual candies
Choose own 3 digit number and draw as many different ways to make that number as you can.
Share students solutions.
Test Preparation for GRADE 4 Mathematics
Week 1
Lesson 4: State Standard: 4N7, 4N9
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 could 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 Share. Test Preparation for GRADE 4 Mathematics
Week 1
Lesson 5: State Standard: 4N7
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 sized 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.
Share solutions.
Show all the different ways you could share one pizza amongst three people. E.g., 1/3 + 1/3 + 1/3 1/2 + 1/6 + 2/6 1/3 + 1/6 + 3/6
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 4 Mathematics
Week 2
Lesson 1: State Standard: 3N14 (Post March Standard) 3N15 (Post March Standard)
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 Overhead or board.
Ask student how to show ½ on one of the diagrams. Get students to explain.
Ask for 1/3 and why. Ask 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 4 Mathematics
Week 2
Lesson 2: State Standard: 4N6
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 a Consonant is worth 1 and a Vowel is worth 3, how much is your name worth?
State Standards Practice: (25 min.)
Ask students which is more and why? (2 + 3) + 5 =? or 2 + (3 + 5) =?
What about (2 x 3) x 5 =? or 2 x (3 x 5) =?
Explain in words. Share.
Have students make up their own multiplication similar. Have them draw a picture to explain.
Eg. (2x3) x 5 = 30
Share. Test Preparation for GRADE 4 Mathematics
Week 2
Lesson 3: State Standard: 4N13
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 am thinking of a number where the digits go Odd, Even, Odd, Even, etc. When I add the digits together, the total is 25. What could my number be?
State Standards Practice: (25 min.) 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 multiply them together. Share findings. (All students should have had an Even Answer) Ask students to choose any two odd numbers and multiply them together. Share findings. (All students should have had an Odd Answer) Ask students to choose one even and one odd number and multiply them together. Share findings. (All students should have had an Even Answer) Have students summarize these findings in their own words.
Preparation for GRADE 4 Mathematics
Week 2
Lesson 4: State Standard: 4N14, 4N15
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 58 monkeys and then I saw 19 more. How many did I see?” Share strategies. (Eg. Counting up 19 by 1’s, Counting up 20 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 students use 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 4 Mathematics
Week 2
Lesson 5: State Standard: 4N16, 3N19, 3N20 (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)
When I placed 10 different numbers in order, the highest was 999 and the lowest was 100. There was a difference of at least 9 between each number. What could the numbers be?
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. Ask students to find what the pattern is with the ones place. (E.g., for the 4’s, 4,8,2,6,0 repeated.) 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 different charts.
Share patterns.
Test Preparation for GRADE 4 Mathematics
Week 3
Lesson 1: State Standard: 3N22 (Grade 3 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)
How many different ways can you make 456?
State Standards Practice: (25 min.) 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) Share.
Students can choose own number. (Multiples of 6 or 12 work well as they have many factors) Share. Test Preparation for GRADE 4 Mathematics
Week 3
Lesson 2: State Standard: 4N18, 4N19, 4N20
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. How many birds could there have been? Draw a Picture, Show the Number Sentence and Explain in words.
State Standards Practice: (25 min.)
Maria said if you know 2 X 4 = 8, its easy to work out 2 X 40, explain.
Share students work.
How could you use this to help with 2 X 43? (2 X 40 = 80 and 2 X 3 = 6, so 80 and 6 is 86)
Use this method to work out 3 x 235.
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.
Test Preparation for GRADE 4 Mathematics
Week 3
Lesson 3: State Standard: 4N21, 4N22
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 made cookies for me and my friends. How many might we have got each if we shared them evenly?
State Standards Practice: (25 min.)
My bag of M&M’s had 24 red ones. I wanted to share them with my friends after school evenly, but I don’t know how many friends there will be. Show how I can share them evenly if there is only me and one friend up to if all 11 friends turn up.
Show how to do this for a number larger than 50 M&M’s (your choice). Test Preparation for GRADE 4 Mathematics
Week 3
Lesson 4: State Standard: 4N16, 4N17
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)
Eight 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: (25 min.)
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.
Ask students to draw representations of all the ways of sharing 18 cookies among their friends. Share.
Test Preparation for GRADE 4 Mathematics
Week 3
Lesson 5: State Standard: 4N27 3N25 (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)
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 each 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. Have students develop their own rule for this.
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 4 Mathematics
Week 4
Lesson 1: State Standard: 3A1 (Post March), 4A2, 4A3
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 is older than his Dog, but younger than his Cat. If his Dogs age has two digits, how old might each be?
State Standards Practice:(25 min.)
Which side of > is larger? Which side is smaller?
Put these numbers on the correct side: (30 + 6) and (10 + 2)  >  (11 + 11) and (11 + 12)  >  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. (1 + 1), (2 + 3), (1 + 4), (2 + 5), (4 + 4 + 1), (5 x 2).  >   <   = 
Share students solutions.
Have students make up own using Money. Have students make up own using Fractions. Share. Test Preparation for GRADE 4 Mathematics
Week 4
Lesson 2: State Standard: 4A4, 4A5
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)
You found a magic pot that doubled everything that you put in it. What would you put in it and why?
State Standards Practice:(25 min.)
Using a 100’s Chart, complete the following pattern for the next 10 numbers.
2, 5, 8,… (+3) 99, 95, 91, … (4) 1, 2, 4, 7, 11, … (+1,+2,+3,…) 2, 4, 8, 16, … (x2)
Share students solutions.
If 5 goes into the machine and 15 comes out, what is the machine doing to the numbers? (adding 12 or x 3) 5 15
What about if the same machine has 4 going in and 12 coming out? (Must be x 3, because cant be adding12)
Make your own machine with 5 examples of what goes in and what comes out.
Share students work.
Test Preparation for GRADE 4 Mathematics
Week 4
Lesson 3: State Standard: 4G1
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 drew a shape with five sides on top of a 4 sided shape between two 3 sided shapes. What might this look like?
State Standards Practice:(25 min.)
If these two figures are Congruent, what might Congruent mean?
If these two figures are Similar, what might similar mean?
Write definitions in your own words.
Complete the following table: (Have students work individually or small groups before sharing)
Share students work. Test Preparation for GRADE 4 Mathematics
Week 4
Lesson 4: State Standard: 3G2 (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) There was a circle on top of a triangle. The Triangle was between a Rhombus and a Trapezoid. It was all surrounded by a Hexagon. What might it have looked like?
State Standards Practice: (25 min.)
If Congruent Dinosaurs are the same size and shape, and similar Dinosaurs are the same shape but a different size, which dinosaurs are congruent and which are similar?
Share findings. Test Preparation for GRADE 4 Mathematics
Week 4
Lesson 5: State Standard: 4G3, 4G4
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)
Draw a shape with a perimeter of 18.
State Standards Practice: (25 min.)
Write your initials in block letters only drawing along the lines. What is the perimeter of each initial? What is the area of each initial?
Draw a picture and count its perimeter and area.
Share.
Test Preparation for GRADE 4 Mathematics
Week 5
Lesson 1: State Standard: 4G5
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:(25 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.
Label a Vertex, Face and Edge on each figure.
Share students work.
Test Preparation for GRADE 4 Mathematics
Week 5
Lesson 2: State Standard: 4M2, 4M4, 4M5, 4M6, 4M7
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 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.)
Measure Length & height (to 1/4 inch & cm.) 4M2 Mass (grams and kilograms) 4M4, 4M5 Capacity (milliliters (ml.s) and liters) 4M6, 4M7
Provide students with access to the following, preferably at least one set per group. · 12 inch & 30cm ruler · Scales to measure grams and kilograms · Measuring cup set (cup, pint, quart, gallon) · 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. Brainstorm how they could do this. (Measure length, height, mass, volume
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 4 Mathematics
Week 5
Lesson 3: State Standard: 4M8, 4M9
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 what time you like to have lunch. Write underneath the clock what this time looks like on a digital clock.
Write what time you like to have dinner. How long is it between having lunch and having dinner? What about between Breakfast and Lunch. Which is longer?
Have students work out how long it is until a) their birthday b) the end of the school year c) dates of their own choosing In both weeks and days, and just days.
Share.
Week 5
Lesson 4: State Standard: 3S2, 3S3, 3S4, 3S5, 3S6, 3S7, 3S8 (Note: All Grade 4 Statistics and Probability Standards are PostMarch) 4S3, 4S5, 4S6
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.
Predict the number of each color in a second bag of M&M’s. Have students record their predictions. Have each student create a tally chart as you say each color as you draw M&M’s from the bag one at a time.
