Cindy Whitehead
@cindywhitehead.bsky.social
Retired Middle School Math Teacher, still dipping my toes in the waters of math every once in awhile.
Honored to be a Desmos Fellow, Cohort 3!
Honored to be a Desmos Fellow, Cohort 3!
LOVE this!!!
Here’s a link to an interactive Geogebra applet by Matthew Ziegler that I ran across YEARS ago that demonstrates this graphical approach ☺️
www.geogebra.org/m/QHgYSXT4
Here’s a link to an interactive Geogebra applet by Matthew Ziegler that I ran across YEARS ago that demonstrates this graphical approach ☺️
www.geogebra.org/m/QHgYSXT4
Simplifying Square Roots
This applet takes a graphical approach to simplifying square roots.
www.geogebra.org
September 24, 2025 at 5:40 AM
LOVE this!!!
Here’s a link to an interactive Geogebra applet by Matthew Ziegler that I ran across YEARS ago that demonstrates this graphical approach ☺️
www.geogebra.org/m/QHgYSXT4
Here’s a link to an interactive Geogebra applet by Matthew Ziegler that I ran across YEARS ago that demonstrates this graphical approach ☺️
www.geogebra.org/m/QHgYSXT4
I do agree there must be some resisters working in puzzles … case in point:
Strands #567
“Stand by me”
🟡🔵🔵🔵
🔵🔵
🤷♀️🤞☺️
Strands #567
“Stand by me”
🟡🔵🔵🔵
🔵🔵
🤷♀️🤞☺️
September 21, 2025 at 1:15 PM
I do agree there must be some resisters working in puzzles … case in point:
Strands #567
“Stand by me”
🟡🔵🔵🔵
🔵🔵
🤷♀️🤞☺️
Strands #567
“Stand by me”
🟡🔵🔵🔵
🔵🔵
🤷♀️🤞☺️
14/40 is equivalent to 7/20, and since 20 is a friendly factor of 100, I can easily find ANOTHER equivalent fraction: 35/100, which is the same as 35% ☺️
July 14, 2025 at 8:57 PM
14/40 is equivalent to 7/20, and since 20 is a friendly factor of 100, I can easily find ANOTHER equivalent fraction: 35/100, which is the same as 35% ☺️
It would be interesting to see the data for the next seven years. While climate change has influenced increasingly occurring climate-related crises, simultaneously, the “climate change hoax” propaganda has ramped up considerably.
Would both blue and red be on an upward trend? 🤔🤷♀️
Would both blue and red be on an upward trend? 🤔🤷♀️
May 17, 2025 at 3:51 PM
It would be interesting to see the data for the next seven years. While climate change has influenced increasingly occurring climate-related crises, simultaneously, the “climate change hoax” propaganda has ramped up considerably.
Would both blue and red be on an upward trend? 🤔🤷♀️
Would both blue and red be on an upward trend? 🤔🤷♀️
I know it’s the next day, but these were lovely prompts!
I am always an advocate of making connections within a concept as well as between concepts to develop deeper understanding!
I am always an advocate of making connections within a concept as well as between concepts to develop deeper understanding!
April 18, 2025 at 3:16 PM
I know it’s the next day, but these were lovely prompts!
I am always an advocate of making connections within a concept as well as between concepts to develop deeper understanding!
I am always an advocate of making connections within a concept as well as between concepts to develop deeper understanding!
Focus on …
4x9x2 is 4 groups of 9x2 (as in the original 4x18) …
or 2 groups of 4x9
(Or even 9 groups of 4x2)
Investigate how to break up that big block of 4x18 into smaller pieces 🤔🤔🤔
4x9x2 is 4 groups of 9x2 (as in the original 4x18) …
or 2 groups of 4x9
(Or even 9 groups of 4x2)
Investigate how to break up that big block of 4x18 into smaller pieces 🤔🤔🤔
April 18, 2025 at 3:13 PM
Focus on …
4x9x2 is 4 groups of 9x2 (as in the original 4x18) …
or 2 groups of 4x9
(Or even 9 groups of 4x2)
Investigate how to break up that big block of 4x18 into smaller pieces 🤔🤔🤔
4x9x2 is 4 groups of 9x2 (as in the original 4x18) …
or 2 groups of 4x9
(Or even 9 groups of 4x2)
Investigate how to break up that big block of 4x18 into smaller pieces 🤔🤔🤔
And then … “oh, these are all ways to decompose 12”
How can we write that?
5x12=5x(6+6)
or 5x(10+2), etc
(Of course, I am also a strong advocate of area models for seeing these connections … big block of 5 by 12 … how can we break it into smaller pieces … how can we represent those pieces)
How can we write that?
5x12=5x(6+6)
or 5x(10+2), etc
(Of course, I am also a strong advocate of area models for seeing these connections … big block of 5 by 12 … how can we break it into smaller pieces … how can we represent those pieces)
April 18, 2025 at 3:05 PM
And then … “oh, these are all ways to decompose 12”
How can we write that?
5x12=5x(6+6)
or 5x(10+2), etc
(Of course, I am also a strong advocate of area models for seeing these connections … big block of 5 by 12 … how can we break it into smaller pieces … how can we represent those pieces)
How can we write that?
5x12=5x(6+6)
or 5x(10+2), etc
(Of course, I am also a strong advocate of area models for seeing these connections … big block of 5 by 12 … how can we break it into smaller pieces … how can we represent those pieces)
I think introducing parentheses too early confuses students - they think “do parentheses first” from Order of Operations.
It’s important for them to notice, for instance, the equivalence of:
5x12 and 5x6+5x6
or …
5x12 and 5x10+5x2
or …
5x12 and 5x8+5x4
even the “less friendly”
5x12 and 5x9+ 5x3
It’s important for them to notice, for instance, the equivalence of:
5x12 and 5x6+5x6
or …
5x12 and 5x10+5x2
or …
5x12 and 5x8+5x4
even the “less friendly”
5x12 and 5x9+ 5x3
April 18, 2025 at 3:01 PM
I think introducing parentheses too early confuses students - they think “do parentheses first” from Order of Operations.
It’s important for them to notice, for instance, the equivalence of:
5x12 and 5x6+5x6
or …
5x12 and 5x10+5x2
or …
5x12 and 5x8+5x4
even the “less friendly”
5x12 and 5x9+ 5x3
It’s important for them to notice, for instance, the equivalence of:
5x12 and 5x6+5x6
or …
5x12 and 5x10+5x2
or …
5x12 and 5x8+5x4
even the “less friendly”
5x12 and 5x9+ 5x3
Cindy Whitehead
Retired HS / MS math teacher
PNW
My daughter came to visit for Easter! ☺️
Retired HS / MS math teacher
PNW
My daughter came to visit for Easter! ☺️
April 18, 2025 at 2:53 PM
Cindy Whitehead
Retired HS / MS math teacher
PNW
My daughter came to visit for Easter! ☺️
Retired HS / MS math teacher
PNW
My daughter came to visit for Easter! ☺️
This is like a “fact family” extension!
5x26
5x(20 +6)
5x20 + 5x6
100 + 30
130
It’s the “partner” to the division!
5x26
5x(20 +6)
5x20 + 5x6
100 + 30
130
It’s the “partner” to the division!
April 18, 2025 at 2:48 PM
This is like a “fact family” extension!
5x26
5x(20 +6)
5x20 + 5x6
100 + 30
130
It’s the “partner” to the division!
5x26
5x(20 +6)
5x20 + 5x6
100 + 30
130
It’s the “partner” to the division!
The concepts of “place value” and “like terms”!
50 + 30 is 80 … similarly, you can “add the 5 and 3” only because they represent 5 tens and 3 tens.
5x + 3x = 8x because there are
“5 x’s and 3 x’s”
50 + 30 is 80 … similarly, you can “add the 5 and 3” only because they represent 5 tens and 3 tens.
5x + 3x = 8x because there are
“5 x’s and 3 x’s”
April 18, 2025 at 2:44 PM
The concepts of “place value” and “like terms”!
50 + 30 is 80 … similarly, you can “add the 5 and 3” only because they represent 5 tens and 3 tens.
5x + 3x = 8x because there are
“5 x’s and 3 x’s”
50 + 30 is 80 … similarly, you can “add the 5 and 3” only because they represent 5 tens and 3 tens.
5x + 3x = 8x because there are
“5 x’s and 3 x’s”
So important for Elem/Secondary teachers to be more aware of what can be /has been done in Elementary that can support deeper understanding and connections to what is learned in secondary!!
COMMUNICATION!
COMMUNICATION!
April 18, 2025 at 2:40 PM
So important for Elem/Secondary teachers to be more aware of what can be /has been done in Elementary that can support deeper understanding and connections to what is learned in secondary!!
COMMUNICATION!
COMMUNICATION!
I notice that blue and black “start with the big numbers”
I wonder if students are done a disservice by always focusing on “starting with the ones”
I wonder if students are done a disservice by always focusing on “starting with the ones”
April 18, 2025 at 2:35 PM
I notice that blue and black “start with the big numbers”
I wonder if students are done a disservice by always focusing on “starting with the ones”
I wonder if students are done a disservice by always focusing on “starting with the ones”
If students “always” go to the typical:
(20+7)(30+3) it becomes almost as rote as the traditional algorithm… 🤔🤔🤔
I like that I can mentally calculate 33x3, but not 33x7 … but 27 is 3 less than 30, so …
(30-3)x33 is
30x33 - 3x33
990 - 99
990 - 90 - 9
900 - 9
891
(20+7)(30+3) it becomes almost as rote as the traditional algorithm… 🤔🤔🤔
I like that I can mentally calculate 33x3, but not 33x7 … but 27 is 3 less than 30, so …
(30-3)x33 is
30x33 - 3x33
990 - 99
990 - 90 - 9
900 - 9
891
April 18, 2025 at 2:32 PM
If students “always” go to the typical:
(20+7)(30+3) it becomes almost as rote as the traditional algorithm… 🤔🤔🤔
I like that I can mentally calculate 33x3, but not 33x7 … but 27 is 3 less than 30, so …
(30-3)x33 is
30x33 - 3x33
990 - 99
990 - 90 - 9
900 - 9
891
(20+7)(30+3) it becomes almost as rote as the traditional algorithm… 🤔🤔🤔
I like that I can mentally calculate 33x3, but not 33x7 … but 27 is 3 less than 30, so …
(30-3)x33 is
30x33 - 3x33
990 - 99
990 - 90 - 9
900 - 9
891
I like breaking 126 into 125 + 1.
8x125 is 1000
(2x125=250, and 4 of those is 1000, but also 1/8=0.125, sticks in my head)
Then there’s just one more 8, so 1008
8x125 is 1000
(2x125=250, and 4 of those is 1000, but also 1/8=0.125, sticks in my head)
Then there’s just one more 8, so 1008
April 18, 2025 at 2:23 PM
I like breaking 126 into 125 + 1.
8x125 is 1000
(2x125=250, and 4 of those is 1000, but also 1/8=0.125, sticks in my head)
Then there’s just one more 8, so 1008
8x125 is 1000
(2x125=250, and 4 of those is 1000, but also 1/8=0.125, sticks in my head)
Then there’s just one more 8, so 1008
I like the purple one for students who might be less fluent with “multiplication facts.”
Breaking one factor into “more parts” might seem like “more work,” but not if they are “friendlier pieces.”
Breaking one factor into “more parts” might seem like “more work,” but not if they are “friendlier pieces.”
April 18, 2025 at 2:18 PM
I like the purple one for students who might be less fluent with “multiplication facts.”
Breaking one factor into “more parts” might seem like “more work,” but not if they are “friendlier pieces.”
Breaking one factor into “more parts” might seem like “more work,” but not if they are “friendlier pieces.”
Don’t parents teach kids what words mean all the time? “Ball” while holding a ball, etc.
Are you implying that kids “know where the vowel goes” and “knows how clauses work” by age five? Aren’t those concepts learned at school?
Are you implying that kids “know where the vowel goes” and “knows how clauses work” by age five? Aren’t those concepts learned at school?
April 16, 2025 at 1:19 AM
Don’t parents teach kids what words mean all the time? “Ball” while holding a ball, etc.
Are you implying that kids “know where the vowel goes” and “knows how clauses work” by age five? Aren’t those concepts learned at school?
Are you implying that kids “know where the vowel goes” and “knows how clauses work” by age five? Aren’t those concepts learned at school?
“Hanging out listening to them talk about math” is not what I meant by a mathematically rich environment. Playing with patterns, shapes, and number concepts with a child can provide the same foundation for learning math that verbal interactions provide for language development.
April 16, 2025 at 1:05 AM
“Hanging out listening to them talk about math” is not what I meant by a mathematically rich environment. Playing with patterns, shapes, and number concepts with a child can provide the same foundation for learning math that verbal interactions provide for language development.
Babies don’t learn language just by “being in the world.” If they are not spoken to / interacted with on a regular basis, their language acquisition by age five would be very minimal. On the other hand, a child who grows up in a mathematically rich environment will be quite fluent by age five.
April 16, 2025 at 12:42 AM
Babies don’t learn language just by “being in the world.” If they are not spoken to / interacted with on a regular basis, their language acquisition by age five would be very minimal. On the other hand, a child who grows up in a mathematically rich environment will be quite fluent by age five.
Trying to avoid spoilers …
What do the hens “do” ? 🤔🤔🤔
What do the hens “do” ? 🤔🤔🤔
March 24, 2025 at 4:37 PM
Trying to avoid spoilers …
What do the hens “do” ? 🤔🤔🤔
What do the hens “do” ? 🤔🤔🤔
Make it friendlier …
104 - 44 …
104 - 4 = 100, then
100 - 40 = 60
But since it was really only 103, the result is one less, so 59
104 - 44 …
104 - 4 = 100, then
100 - 40 = 60
But since it was really only 103, the result is one less, so 59
March 17, 2025 at 9:18 PM
Make it friendlier …
104 - 44 …
104 - 4 = 100, then
100 - 40 = 60
But since it was really only 103, the result is one less, so 59
104 - 44 …
104 - 4 = 100, then
100 - 40 = 60
But since it was really only 103, the result is one less, so 59
Each step adds one more row of 3 to the bottom, and an extra “one more flower” on the top.
Step 4 would have 4 rows of 3 flowers as well as just 3 “sticking out of the top” (4x3+3)
Step 25 would have 25 rows of 3 flowers and 24 more flowers sticking up at the top.” (25x3 + 24)
Step 4 would have 4 rows of 3 flowers as well as just 3 “sticking out of the top” (4x3+3)
Step 25 would have 25 rows of 3 flowers and 24 more flowers sticking up at the top.” (25x3 + 24)
March 14, 2025 at 1:41 AM
Each step adds one more row of 3 to the bottom, and an extra “one more flower” on the top.
Step 4 would have 4 rows of 3 flowers as well as just 3 “sticking out of the top” (4x3+3)
Step 25 would have 25 rows of 3 flowers and 24 more flowers sticking up at the top.” (25x3 + 24)
Step 4 would have 4 rows of 3 flowers as well as just 3 “sticking out of the top” (4x3+3)
Step 25 would have 25 rows of 3 flowers and 24 more flowers sticking up at the top.” (25x3 + 24)
I think of 45° angles … 8 45’s makes an entire revolution … 360☺️
March 3, 2025 at 11:28 PM
I think of 45° angles … 8 45’s makes an entire revolution … 360☺️