# Math With Amar Academy — brand kit and 14-day teaching campaign Prepared September 23, 2026. These materials do not claim that accounts or posts are already published, or that usernames are available. ## Profile setup 1. Create or open your own TikTok, YouTube, Facebook, and Instagram profiles. 2. Use **Math With Amar Academy** as the display name. Check **@mathwithamaracademy** in each platform; availability is unverified. Choose a consistent available variation if needed. 3. Upload the portrait and check its circular crop. 4. Paste the short bio and matching website link below. Use the longer description where suitable. 5. Record an introduction and a useful explanation, add captions, preview, and publish from your own account. Young learners can use these activities with a parent or caregiver; do not ask children to create social profiles. Short bio: Math made clear. Free lessons + practice. mathwithamar.com/learn Longer description: Understand the idea. See the steps. Try it yourself. Math With Amar Academy shares free lessons, visual explanations, and practice from Grade 1 to graduate topics. Choose your level at mathwithamar.com/learn. Parents and adult learners can contact Amar about tutoring. ## Brand assets - [Profile JPG, 1024 pixels](https://www.mathwithamar.com/academy/amar-profile-1024.jpg) - [Original profile PNG](https://www.mathwithamar.com/academy/amar-profile.png) - Portrait: Amar’s own photograph edited with AI; it is not evidence of an event, award, or credential. - Colors: deep navy #102D32, teal #067B79, warm cream #F7F5ED. - Promise: Understand the idea. See the steps. Try it yourself. - Style: calm, direct, specific. Explain before inviting people to practice. ## Website links ### TikTok https://www.mathwithamar.com/learn?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch Add the website link if your account has a Website field. Otherwise show mathwithamar.com/learn on screen and in your profile text. ### YouTube Shorts https://www.mathwithamar.com/learn?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch Add the website to your channel profile links. Ordinary URLs in Shorts descriptions and comments are not clickable; show mathwithamar.com/learn on screen. ### Facebook https://www.mathwithamar.com/learn?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch Put the lesson link in the Page post and the academy link in your Page website field. Preview the link and image before posting. ### Instagram https://www.mathwithamar.com/learn?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch Add the academy website in your profile links. Point the Reel caption to that profile link and show mathwithamar.com/learn on screen. These fixed source/medium/campaign labels contain no personal details. Ordinary analytics reports pages and available referrers. Vercel UTM filters require a paid analytics tier. Privacy opt-outs and missing referrers limit attribution; labels alone do not prove that a visit, lead, or sale was measured. ## Six ready graphics ### A 5% hill is not a 5° hill - [Square PNG, 1080 × 1080](https://www.mathwithamar.com/promotion/road-grade-square.png) - [Story PNG, 1080 × 1920](https://www.mathwithamar.com/promotion/road-grade-story.png) - [Square SVG](https://www.mathwithamar.com/promotion/road-grade-square.svg) · [Story SVG](https://www.mathwithamar.com/promotion/road-grade-story.svg) Image description: A 5 percent road grade rises 5 metres over 100 horizontal metres. Its angle is about 2.86 degrees. Diagram not to scale. ### The changing base of a percentage - [Square PNG, 1080 × 1080](https://www.mathwithamar.com/promotion/sale-math-square.png) - [Story PNG, 1080 × 1920](https://www.mathwithamar.com/promotion/sale-math-story.png) - [Square SVG](https://www.mathwithamar.com/promotion/sale-math-square.svg) · [Story SVG](https://www.mathwithamar.com/promotion/sale-math-story.svg) Image description: An 80 dollar item with 25 percent off costs 60 dollars. Adding 8 percent tax to the sale price gives 64 dollars and 80 cents. ### Same fence. Different space. - [Square PNG, 1080 × 1080](https://www.mathwithamar.com/promotion/fence-area-square.png) - [Story PNG, 1080 × 1920](https://www.mathwithamar.com/promotion/fence-area-story.png) - [Square SVG](https://www.mathwithamar.com/promotion/fence-area-square.svg) · [Story SVG](https://www.mathwithamar.com/promotion/fence-area-story.svg) Image description: Two rectangles both have a perimeter of 40 metres. A 6 by 14 metre rectangle has area 84 square metres. A 10 by 10 metre square has area 100 square metres. ## Before filming Use a clean original vertical recording, a quiet room, and equations large enough for a phone. Give a complete explanation, label units and assumptions, and leave a pause for thinking. Add readable captions and use media/audio you own or are licensed to publish. Keep students’ names, faces, and private work out of the video. A translated version needs a human review of meaning and notation. Estimated lengths below are not timed final videos. ## 14-day overview | Day | Audience | Teaching point | | --- | --- | --- | | 1 | Grade 1 · for families | Count the objects, not their arrangement | | 2 | Grade 2 · place value | The zero that holds a place | | 3 | Grade 3 · multiplication | Turn a picture into a multiplication proof | | 4 | Grade 4 · fractions | Different fraction, same amount | | 5 | Grade 6 · ratios | Keep the mix the same | | 6 | High school · slope and angles | The road sign that fools your intuition | | 7 | Grades 6–8 · percentages | A discount and tax do not cancel | | 8 | High school · geometry to calculus | Can the same fence enclose more space? | | 9 | Grades 7–9 · algebra | A budget becomes an inequality | | 10 | High school · trigonometry | Measure a tree without climbing it | | 11 | Grades 7–12 · statistics | The average hides the variation | | 12 | Undergraduate · calculus | The water already in the tank counts | | 13 | Undergraduate · linear algebra | A derivative hiding inside a matrix | | 14 | Graduate bridge · analysis and fluids | An average-size bound can miss a growing peak | ## Complete scripts and captions ### Day 1: Count the objects, not their arrangement Audience: Grade 1 · for families Format: 20–30 second overhead demonstration Hook: If I spread these seven counters out, do I have more? Visual plan: Use large counters on a plain mat. Touch each once, move the same seven apart, and display 4 + 3 = 7. Keep the full set visible throughout. Spoken script: Here are four counters and three more. Touch each counter once: one, two, three, four, five, six, seven. Now spread them farther apart. Nothing was added or removed, so there are still seven. The last counting word tells how many objects we have. Families can try the count-once lesson together at Math With Amar Academy. Publish step: Introduce the academy with a useful demonstration. Address parents and caregivers; do not ask young children to create social accounts. **TikTok caption** If I spread these seven counters out, do I have more? 4 counters + 3 counters = 7. Moving them changes the spacing, not the number. Try touching each object exactly once, then rearranging the same collection. Families: open the free lesson and try the next example together. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g1-count-once?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #EarlyMath #LearningTogether **YouTube Shorts caption** If I spread these seven counters out, do I have more? 4 counters + 3 counters = 7. Moving them changes the spacing, not the number. Try touching each object exactly once, then rearranging the same collection. Families: open the free lesson and try the next example together. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g1-count-once?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #EarlyMath #LearningTogether **Facebook caption** If I spread these seven counters out, do I have more? 4 counters + 3 counters = 7. Moving them changes the spacing, not the number. Try touching each object exactly once, then rearranging the same collection. Families: open the free lesson and try the next example together. Full free lesson: https://www.mathwithamar.com/learn/g1-count-once?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #EarlyMath #LearningTogether **Instagram caption** If I spread these seven counters out, do I have more? 4 counters + 3 counters = 7. Moving them changes the spacing, not the number. Try touching each object exactly once, then rearranging the same collection. Families: open the free lesson and try the next example together. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g1-count-once?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #EarlyMath #LearningTogether ### Day 2: The zero that holds a place Audience: Grade 2 · place value Format: 25–35 second place-value board Hook: Why is 507 different from 57 if zero means none? Visual plan: Label H, T, O in words as well as letters. Put 5, 0, 7 below them, then compare 57 aligned to the right. Show 500 versus 50. Spoken script: Write three columns: hundreds, tens, ones. Five hundred seven has five hundreds, no tens, and seven ones. That is five hundred plus zero plus seven. The zero keeps the five in the hundreds column. Remove it from the written number and fifty-seven has five tens instead. Try building another number with an empty place in the free lesson. Publish step: Use the same portrait and display name as day one. Add captions for the spoken place names. **TikTok caption** Why is 507 different from 57 if zero means none? 507 = 500 + 0 + 7. In 57, the 5 means 50; in 507 it means 500. A zero can hold an empty place without making the other digits move. Try the worked example and practice questions. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g2-expanded-form?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #PlaceValue #PrimaryMath **YouTube Shorts caption** Why is 507 different from 57 if zero means none? 507 = 500 + 0 + 7. In 57, the 5 means 50; in 507 it means 500. A zero can hold an empty place without making the other digits move. Try the worked example and practice questions. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g2-expanded-form?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #PlaceValue #PrimaryMath **Facebook caption** Why is 507 different from 57 if zero means none? 507 = 500 + 0 + 7. In 57, the 5 means 50; in 507 it means 500. A zero can hold an empty place without making the other digits move. Try the worked example and practice questions. Full free lesson: https://www.mathwithamar.com/learn/g2-expanded-form?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #PlaceValue #PrimaryMath **Instagram caption** Why is 507 different from 57 if zero means none? 507 = 500 + 0 + 7. In 57, the 5 means 50; in 507 it means 500. A zero can hold an empty place without making the other digits move. Try the worked example and practice questions. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g2-expanded-form?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #PlaceValue #PrimaryMath ### Day 3: Turn a picture into a multiplication proof Audience: Grade 3 · multiplication Format: 25–35 second dot-array demonstration Hook: Can you prove 4 × 7 equals 7 × 4 without counting twice? Visual plan: Use a real sheet with a 4-by-7 dot array. Label rows and dots per row, rotate the sheet, and relabel. Avoid an animation that accidentally adds dots. Spoken script: Draw four rows of seven dots. That is twenty-eight dots. Turn the paper a quarter turn. Now you can see seven rows of four. The same dots are still there; we did not add or remove any. This shows why four times seven equals seven times four. Make your own array and try the practice in the lesson. Publish step: Pause briefly before turning the array so viewers can predict the new row count. Link to practice, not an answer hidden in another post. **TikTok caption** Can you prove 4 × 7 equals 7 × 4 without counting twice? 4 rows × 7 dots = 28 dots. Turn the same array: 7 rows × 4 dots = 28. The total stays the same because the objects stay the same. Draw another rectangle of dots and test the idea. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g3-turn-array?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Multiplication #VisualMath **YouTube Shorts caption** Can you prove 4 × 7 equals 7 × 4 without counting twice? 4 rows × 7 dots = 28 dots. Turn the same array: 7 rows × 4 dots = 28. The total stays the same because the objects stay the same. Draw another rectangle of dots and test the idea. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g3-turn-array?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Multiplication #VisualMath **Facebook caption** Can you prove 4 × 7 equals 7 × 4 without counting twice? 4 rows × 7 dots = 28 dots. Turn the same array: 7 rows × 4 dots = 28. The total stays the same because the objects stay the same. Draw another rectangle of dots and test the idea. Full free lesson: https://www.mathwithamar.com/learn/g3-turn-array?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Multiplication #VisualMath **Instagram caption** Can you prove 4 × 7 equals 7 × 4 without counting twice? 4 rows × 7 dots = 28 dots. Turn the same array: 7 rows × 4 dots = 28. The total stays the same because the objects stay the same. Draw another rectangle of dots and test the idea. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g3-turn-array?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Multiplication #VisualMath ### Day 4: Different fraction, same amount Audience: Grade 4 · fractions Format: 30–40 second shaded-strip explanation Hook: How can six eighths become three fourths without losing anything? Visual plan: Use one rectangle throughout. Add eight equal divisions, shade six, then place a bold outline around each pair. Keep the outer boundary fixed. Spoken script: Split one strip into eight equal pieces and shade six. Now group the pieces in pairs. The whole strip has four pairs, and three pairs are shaded. Each pair is one fourth of the original whole, so six eighths is three fourths. The shaded area has not changed; the unit has. Try another regrouping in the free lesson. Publish step: Offer an image description in the caption so the fraction explanation also works without relying on color. **TikTok caption** How can six eighths become three fourths without losing anything? 6/8 = 3/4: divide both the selected-piece count and the total-piece count by 2. Keep the same whole. Larger pieces need fewer pieces to describe the same shaded amount. Try the next fraction in the lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g4-simplify-fractions?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Fractions #VisualLearning **YouTube Shorts caption** How can six eighths become three fourths without losing anything? 6/8 = 3/4: divide both the selected-piece count and the total-piece count by 2. Keep the same whole. Larger pieces need fewer pieces to describe the same shaded amount. Try the next fraction in the lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g4-simplify-fractions?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Fractions #VisualLearning **Facebook caption** How can six eighths become three fourths without losing anything? 6/8 = 3/4: divide both the selected-piece count and the total-piece count by 2. Keep the same whole. Larger pieces need fewer pieces to describe the same shaded amount. Try the next fraction in the lesson. Full free lesson: https://www.mathwithamar.com/learn/g4-simplify-fractions?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Fractions #VisualLearning **Instagram caption** How can six eighths become three fourths without losing anything? 6/8 = 3/4: divide both the selected-piece count and the total-piece count by 2. Keep the same whole. Larger pieces need fewer pieces to describe the same shaded amount. Try the next fraction in the lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g4-simplify-fractions?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Fractions #VisualLearning ### Day 5: Keep the mix the same Audience: Grade 6 · ratios Format: 30–40 second ratio-table explanation Hook: Two measures blue, five white. What if the white becomes twenty? Visual plan: Draw a two-column ratio table: Blue 2, 8; White 5, 20. Put ×4 beside both columns. Use labeled measures so the model is clear. Spoken script: Our model mix has two measures of blue for five of white. Twenty white is four times five, so multiply the blue by four too: two times four is eight. The matching pair is eight blue and twenty white. Adding fifteen to both amounts would change the ratio. Try extending the table in the free lesson. Publish step: Answer one common mathematical misconception in the caption. Keep responses general and avoid collecting student details. **TikTok caption** Two measures blue, five white. What if the white becomes twenty? 2:5 scales to 8:20 because both quantities are multiplied by 4. Equal scaling preserves the ratio; equal addition generally does not. This is a mathematical mixing model. Extend the table in the lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g6-equivalent-ratio-table?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Ratios #MiddleSchoolMath **YouTube Shorts caption** Two measures blue, five white. What if the white becomes twenty? 2:5 scales to 8:20 because both quantities are multiplied by 4. Equal scaling preserves the ratio; equal addition generally does not. This is a mathematical mixing model. Extend the table in the lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g6-equivalent-ratio-table?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Ratios #MiddleSchoolMath **Facebook caption** Two measures blue, five white. What if the white becomes twenty? 2:5 scales to 8:20 because both quantities are multiplied by 4. Equal scaling preserves the ratio; equal addition generally does not. This is a mathematical mixing model. Extend the table in the lesson. Full free lesson: https://www.mathwithamar.com/learn/g6-equivalent-ratio-table?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Ratios #MiddleSchoolMath **Instagram caption** Two measures blue, five white. What if the white becomes twenty? 2:5 scales to 8:20 because both quantities are multiplied by 4. Equal scaling preserves the ratio; equal addition generally does not. This is a mathematical mixing model. Extend the table in the lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/g6-equivalent-ratio-table?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Ratios #MiddleSchoolMath ### Day 6: The road sign that fools your intuition Audience: High school · slope and angles Format: 25–35 second video; road-grade square or story card Hook: Does a 5% road grade mean a 5-degree hill? Visual plan: Draw a road triangle. Label 5 m rise and 100 m horizontal run. Pause on the question, then reveal 2.86°. Say the sketch is not to scale. Spoken script: A 5% road grade means a rise of 5 metres for every 100 horizontal metres. That ratio is 5 divided by 100, or 0.05. To get the angle, use inverse tangent: arctan of 0.05 is about 2.86 degrees. A percent grade and an angle measure different things. Try the worked example at Math With Amar. Publish step: Set the profile website link to the matching platform link above; publish the full explanation and save a baseline of views and website visits. **TikTok caption** Does a 5% road grade mean a 5-degree hill? A 5% road grade rises 5 m for every 100 horizontal metres. Its angle is arctan(0.05), about 2.86° — not 5°. Sketch a triangle and label the horizontal run first. Free explanation and practice at Math With Amar. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/slope-and-road-grade?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #MathInRealLife #Algebra **YouTube Shorts caption** Does a 5% road grade mean a 5-degree hill? A 5% road grade rises 5 m for every 100 horizontal metres. Its angle is arctan(0.05), about 2.86° — not 5°. Sketch a triangle and label the horizontal run first. Free explanation and practice at Math With Amar. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/slope-and-road-grade?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #MathInRealLife #Algebra **Facebook caption** Does a 5% road grade mean a 5-degree hill? A 5% road grade rises 5 m for every 100 horizontal metres. Its angle is arctan(0.05), about 2.86° — not 5°. Sketch a triangle and label the horizontal run first. Free explanation and practice at Math With Amar. Full free lesson: https://www.mathwithamar.com/learn/slope-and-road-grade?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #MathInRealLife #Algebra **Instagram caption** Does a 5% road grade mean a 5-degree hill? A 5% road grade rises 5 m for every 100 horizontal metres. Its angle is arctan(0.05), about 2.86° — not 5°. Sketch a triangle and label the horizontal run first. Free explanation and practice at Math With Amar. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/slope-and-road-grade?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #MathInRealLife #Algebra ### Day 7: A discount and tax do not cancel Audience: Grades 6–8 · percentages Format: 25–35 second video; sale-math square or story card Hook: $80, then 25% off, then 8% tax. What do you pay? Visual plan: Write $80 → $60 → $64.80 on separate cards. Under each arrow show ×0.75, then ×1.08. State the assumed tax order. Spoken script: Start with eighty dollars. Taking off twenty-five percent leaves seventy-five percent, so eighty times 0.75 is sixty dollars. In this example, the eight-percent tax applies to the sale price. Sixty times 1.08 is sixty-four dollars and eighty cents. The percentage base changes after the discount. Work through another example at Math With Amar. Publish step: Post the story graphic alongside the video. Record which question viewers ask about the changing percentage base. **TikTok caption** $80, then 25% off, then 8% tax. What do you pay? $80 × 0.75 × 1.08 = $64.80. This example applies 8% tax after the 25% discount, so the tax is calculated on $60. The lesson: name the base before using a percentage. Try the free worked example. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/percentages-discounts-and-tax?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Percentages #EverydayMath **YouTube Shorts caption** $80, then 25% off, then 8% tax. What do you pay? $80 × 0.75 × 1.08 = $64.80. This example applies 8% tax after the 25% discount, so the tax is calculated on $60. The lesson: name the base before using a percentage. Try the free worked example. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/percentages-discounts-and-tax?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Percentages #EverydayMath **Facebook caption** $80, then 25% off, then 8% tax. What do you pay? $80 × 0.75 × 1.08 = $64.80. This example applies 8% tax after the 25% discount, so the tax is calculated on $60. The lesson: name the base before using a percentage. Try the free worked example. Full free lesson: https://www.mathwithamar.com/learn/percentages-discounts-and-tax?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Percentages #EverydayMath **Instagram caption** $80, then 25% off, then 8% tax. What do you pay? $80 × 0.75 × 1.08 = $64.80. This example applies 8% tax after the 25% discount, so the tax is calculated on $60. The lesson: name the base before using a percentage. Try the free worked example. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/percentages-discounts-and-tax?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Percentages #EverydayMath ### Day 8: Can the same fence enclose more space? Audience: High school · geometry to calculus Format: 30–40 second video; fence-area square or story card Hook: Both gardens use 40 metres of fence. Which has more space? Visual plan: Draw both rectangles on squared paper using the same scale. Trace the boundary, then shade the area. End with 84 m² versus 100 m². Spoken script: A six-by-fourteen rectangle has a perimeter of forty metres and area eighty-four square metres. A ten-by-ten square has the same perimeter, but its area is one hundred square metres. That is sixteen square metres more space. With a fixed forty-metre perimeter and four straight sides forming a rectangle, the square gives the maximum area. See the calculus explanation at Math With Amar. Publish step: Ask viewers which dimensions they would try next. Link the full lesson for learners who want the derivative proof. **TikTok caption** Both gardens use 40 metres of fence. Which has more space? 6 × 14 = 84 m². 10 × 10 = 100 m². Both rectangles use 40 m of fence, but the square has 16 m² more area. Same perimeter does not mean same area. The full lesson explains why the square maximizes area among rectangles with this perimeter. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/derivatives-and-maximum-area?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Geometry #Calculus **YouTube Shorts caption** Both gardens use 40 metres of fence. Which has more space? 6 × 14 = 84 m². 10 × 10 = 100 m². Both rectangles use 40 m of fence, but the square has 16 m² more area. Same perimeter does not mean same area. The full lesson explains why the square maximizes area among rectangles with this perimeter. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/derivatives-and-maximum-area?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Geometry #Calculus **Facebook caption** Both gardens use 40 metres of fence. Which has more space? 6 × 14 = 84 m². 10 × 10 = 100 m². Both rectangles use 40 m of fence, but the square has 16 m² more area. Same perimeter does not mean same area. The full lesson explains why the square maximizes area among rectangles with this perimeter. Full free lesson: https://www.mathwithamar.com/learn/derivatives-and-maximum-area?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Geometry #Calculus **Instagram caption** Both gardens use 40 metres of fence. Which has more space? 6 × 14 = 84 m². 10 × 10 = 100 m². Both rectangles use 40 m of fence, but the square has 16 m² more area. Same perimeter does not mean same area. The full lesson explains why the square maximizes area among rectangles with this perimeter. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/derivatives-and-maximum-area?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Geometry #Calculus ### Day 9: A budget becomes an inequality Audience: Grades 7–9 · algebra Format: 25–35 second whiteboard video Hook: $36 upfront and $8 per visit. How far does $100 go? Visual plan: Show $100 budget, remove the $36 fixed cost, then divide the $64 remainder into eight $8 groups. Keep dollars and visits labeled. Spoken script: Write the cost as thirty-six plus eight times the number of visits. Our budget is one hundred dollars, so thirty-six plus eight v is at most one hundred. Subtract thirty-six, then divide by eight: v is at most eight. Since visits are whole numbers, eight is the maximum. Check: eight visits cost one hundred dollars; nine cost one hundred eight. Try the budget lesson at Math With Amar. Publish step: Record a close-up board take with large writing. Put the worked answer in the video, not only in a follow-up post. **TikTok caption** $36 upfront and $8 per visit. How far does $100 go? $36 + $8v ≤ $100 gives v ≤ 8. Eight whole visits cost exactly $100; nine cost $108. An inequality turns a budget into a clear limit. Try the free lesson and its practice questions. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/linear-equations-and-a-budget?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Algebra #MathPractice **YouTube Shorts caption** $36 upfront and $8 per visit. How far does $100 go? $36 + $8v ≤ $100 gives v ≤ 8. Eight whole visits cost exactly $100; nine cost $108. An inequality turns a budget into a clear limit. Try the free lesson and its practice questions. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/linear-equations-and-a-budget?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Algebra #MathPractice **Facebook caption** $36 upfront and $8 per visit. How far does $100 go? $36 + $8v ≤ $100 gives v ≤ 8. Eight whole visits cost exactly $100; nine cost $108. An inequality turns a budget into a clear limit. Try the free lesson and its practice questions. Full free lesson: https://www.mathwithamar.com/learn/linear-equations-and-a-budget?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Algebra #MathPractice **Instagram caption** $36 upfront and $8 per visit. How far does $100 go? $36 + $8v ≤ $100 gives v ≤ 8. Eight whole visits cost exactly $100; nine cost $108. An inequality turns a budget into a clear limit. Try the free lesson and its practice questions. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/linear-equations-and-a-budget?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Algebra #MathPractice ### Day 10: Measure a tree without climbing it Audience: High school · trigonometry Format: 30–45 second diagram video Hook: You are 20 metres from a tree. Can one angle estimate its height? Visual plan: Sketch level ground, a tree, a 20 m horizontal distance, and an eye-level line. Label the 35° angle and add the 1.6 m eye height visibly. Spoken script: Assume level ground. The angle from your eye-level horizontal to the tree top is thirty-five degrees. Tangent gives the rise above your eyes: twenty times tan of thirty-five degrees, about fourteen metres. If your eyes are 1.6 metres above the ground, add that too. The tree is about 15.6 metres tall. Use degree mode and treat this as a model estimate. Find the diagram at Math With Amar. Publish step: Use a diagram or film safely from ground level. Link the lesson's assumptions with the answer. **TikTok caption** You are 20 metres from a tree. Can one angle estimate its height? On level ground: tree height ≈ 20 tan(35°) + 1.6 = 15.6 m. The tangent calculation finds the rise above eye level, so eye height matters. This is a teaching model, not a survey measurement. Explore the free trigonometry lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/trigonometry-and-height?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Trigonometry #RealWorldMath **YouTube Shorts caption** You are 20 metres from a tree. Can one angle estimate its height? On level ground: tree height ≈ 20 tan(35°) + 1.6 = 15.6 m. The tangent calculation finds the rise above eye level, so eye height matters. This is a teaching model, not a survey measurement. Explore the free trigonometry lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/trigonometry-and-height?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Trigonometry #RealWorldMath **Facebook caption** You are 20 metres from a tree. Can one angle estimate its height? On level ground: tree height ≈ 20 tan(35°) + 1.6 = 15.6 m. The tangent calculation finds the rise above eye level, so eye height matters. This is a teaching model, not a survey measurement. Explore the free trigonometry lesson. Full free lesson: https://www.mathwithamar.com/learn/trigonometry-and-height?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Trigonometry #RealWorldMath **Instagram caption** You are 20 metres from a tree. Can one angle estimate its height? On level ground: tree height ≈ 20 tan(35°) + 1.6 = 15.6 m. The tangent calculation finds the rise above eye level, so eye height matters. This is a teaching model, not a survey measurement. Explore the free trigonometry lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/trigonometry-and-height?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Trigonometry #RealWorldMath ### Day 11: The average hides the variation Audience: Grades 7–12 · statistics Format: 25–35 second table video Hook: Two groups average 10. Are they equally consistent? Visual plan: Place both triples on the same number line. Mark the shared mean at 10, then show each group's minimum and maximum. Spoken script: Group A is nine, ten, eleven. Group B is zero, ten, twenty. Each adds to thirty, so both have mean ten. But A has a range of two while B has a range of twenty. The same mean can hide very different spreads. A typical value is only one part of the story. Explore mean and spread at Math With Amar. Publish step: Use one shared number-line scale so the spread comparison is fair. Record profile visits alongside video views. **TikTok caption** Two groups average 10. Are they equally consistent? 9, 10, 11 and 0, 10, 20 both have mean 10. Their ranges are 2 and 20. Averages alone do not tell you how consistent a set of observations is. This short uses a small example; the linked lesson develops the idea with another data set. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/statistics-same-average-different-consistency?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Statistics #DataLiteracy **YouTube Shorts caption** Two groups average 10. Are they equally consistent? 9, 10, 11 and 0, 10, 20 both have mean 10. Their ranges are 2 and 20. Averages alone do not tell you how consistent a set of observations is. This short uses a small example; the linked lesson develops the idea with another data set. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/statistics-same-average-different-consistency?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Statistics #DataLiteracy **Facebook caption** Two groups average 10. Are they equally consistent? 9, 10, 11 and 0, 10, 20 both have mean 10. Their ranges are 2 and 20. Averages alone do not tell you how consistent a set of observations is. This short uses a small example; the linked lesson develops the idea with another data set. Full free lesson: https://www.mathwithamar.com/learn/statistics-same-average-different-consistency?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Statistics #DataLiteracy **Instagram caption** Two groups average 10. Are they equally consistent? 9, 10, 11 and 0, 10, 20 both have mean 10. Their ranges are 2 and 20. Averages alone do not tell you how consistent a set of observations is. This short uses a small example; the linked lesson develops the idea with another data set. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/statistics-same-average-different-consistency?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Statistics #DataLiteracy ### Day 12: The water already in the tank counts Audience: Undergraduate · calculus Format: 35–45 second diagram video Hook: The inflow speeds up. How much water is in the tank after four minutes? Visual plan: Draw rate versus time from (0, 2) to (4, 14), shade the trapezoid, and label 32 L added. Draw a separate 5 L starting amount before revealing 37 L. Spoken script: A tank starts with five litres. For four minutes, water enters at two plus three t litres per minute, with no outflow. The rate rises linearly from two to fourteen, so its average is eight litres per minute. Eight times four gives thirty-two litres added. Add the original five: the tank holds thirty-seven litres. The full lesson connects this to a definite integral at Math With Amar. Publish step: Compare post views, profile visits, and observed website traffic. Lesson completions stay on learners’ devices, so the visitor dashboard does not measure them. **TikTok caption** The inflow speeds up. How much water is in the tank after four minutes? For q(t) = 2 + 3t L/min on 0 ≤ t ≤ 4, the linear rate averages (2 + 14)/2 = 8 L/min. That adds 32 L. With 5 L initially and no outflow, the total is 37 L. The integral measures the change; remember the starting amount. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/calculus-flow-rates-and-accumulated-volume?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Calculus #LearnMath **YouTube Shorts caption** The inflow speeds up. How much water is in the tank after four minutes? For q(t) = 2 + 3t L/min on 0 ≤ t ≤ 4, the linear rate averages (2 + 14)/2 = 8 L/min. That adds 32 L. With 5 L initially and no outflow, the total is 37 L. The integral measures the change; remember the starting amount. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/calculus-flow-rates-and-accumulated-volume?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Calculus #LearnMath **Facebook caption** The inflow speeds up. How much water is in the tank after four minutes? For q(t) = 2 + 3t L/min on 0 ≤ t ≤ 4, the linear rate averages (2 + 14)/2 = 8 L/min. That adds 32 L. With 5 L initially and no outflow, the total is 37 L. The integral measures the change; remember the starting amount. Full free lesson: https://www.mathwithamar.com/learn/calculus-flow-rates-and-accumulated-volume?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Calculus #LearnMath **Instagram caption** The inflow speeds up. How much water is in the tank after four minutes? For q(t) = 2 + 3t L/min on 0 ≤ t ≤ 4, the linear rate averages (2 + 14)/2 = 8 L/min. That adds 32 L. With 5 L initially and no outflow, the total is 37 L. The integral measures the change; remember the starting amount. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/calculus-flow-rates-and-accumulated-volume?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #Calculus #LearnMath ### Day 13: A derivative hiding inside a matrix Audience: Undergraduate · linear algebra Format: 40–55 second board explanation Hook: Can a matrix differentiate 3 + 4x + 5x²? Visual plan: Keep the ordered basis visible. Build one matrix column at a time from D(1), D(x), and D(x²). Finish by comparing with the ordinary derivative. Spoken script: Use the basis one, x, x squared. The polynomial becomes the coefficient vector three, four, five. Differentiation sends one to zero, x to one, and x squared to two x. Put those output coordinates in the matrix columns. Reading across its rows gives zero one zero; zero zero two; zero zero zero. Multiplying gives four, ten, zero, which represents four plus ten x. Check the full matrix example in the lesson. Publish step: Film a separate slower explanation if the matrix is hard to read. Short duration is useful only when the reasoning remains clear. **TikTok caption** Can a matrix differentiate 3 + 4x + 5x²? In the ordered basis (1, x, x²), D = [[0,1,0],[0,0,2],[0,0,0]]. D(3,4,5)ᵀ = (4,10,0)ᵀ, representing 4 + 10x. Basis images are columns. Try finding the kernel in the free lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/ug-linear-map-polynomials?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #LinearAlgebra #Calculus **YouTube Shorts caption** Can a matrix differentiate 3 + 4x + 5x²? In the ordered basis (1, x, x²), D = [[0,1,0],[0,0,2],[0,0,0]]. D(3,4,5)ᵀ = (4,10,0)ᵀ, representing 4 + 10x. Basis images are columns. Try finding the kernel in the free lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/ug-linear-map-polynomials?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #LinearAlgebra #Calculus **Facebook caption** Can a matrix differentiate 3 + 4x + 5x²? In the ordered basis (1, x, x²), D = [[0,1,0],[0,0,2],[0,0,0]]. D(3,4,5)ᵀ = (4,10,0)ᵀ, representing 4 + 10x. Basis images are columns. Try finding the kernel in the free lesson. Full free lesson: https://www.mathwithamar.com/learn/ug-linear-map-polynomials?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #LinearAlgebra #Calculus **Instagram caption** Can a matrix differentiate 3 + 4x + 5x²? In the ordered basis (1, x, x²), D = [[0,1,0],[0,0,2],[0,0,0]]. D(3,4,5)ᵀ = (4,10,0)ᵀ, representing 4 + 10x. Basis images are columns. Try finding the kernel in the free lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/ug-linear-map-polynomials?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #LinearAlgebra #Calculus ### Day 14: An average-size bound can miss a growing peak Audience: Graduate bridge · analysis and fluids Format: 40–55 second graph explanation Hook: Can a function keep the same squared integral while its peak grows? Visual plan: Draw narrow rectangles with heights 1, 2, 4 and widths 1, 1/4, 1/16. Label the area under the squared function as 1; do not label the area under the original function as 1. Spoken script: Here is a one-dimensional toy example, not a fluid solution. For positive whole numbers n, a function equals n on an interval of length one over n squared and zero elsewhere. Its squared integral is n squared times one over n squared, which is one. But its maximum value is n, and that grows. So an L-two bound alone does not bound the peak. The linked graduate lesson explores the same distinction with smooth functions in three dimensions. Publish step: Review two weeks of posts and observed website traffic. Choose the explanation with the strongest useful response for a follow-up; record only verified post and inquiry counts. **TikTok caption** Can a function keep the same squared integral while its peak grows? Toy model: fₙ = n on an interval of length 1/n², and 0 elsewhere. ∫|fₙ|² = 1 while ||fₙ||∞ = n. This illustrates a norm distinction, not a Navier–Stokes solution or a proof of blow-up. Explore the smooth 3D example in the graduate lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/grad-fluid-regularity-norms?utm_source=tiktok&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #RealAnalysis #FluidMathematics **YouTube Shorts caption** Can a function keep the same squared integral while its peak grows? Toy model: fₙ = n on an interval of length 1/n², and 0 elsewhere. ∫|fₙ|² = 1 while ||fₙ||∞ = n. This illustrates a norm distinction, not a Navier–Stokes solution or a proof of blow-up. Explore the smooth 3D example in the graduate lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/grad-fluid-regularity-norms?utm_source=youtube&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #RealAnalysis #FluidMathematics **Facebook caption** Can a function keep the same squared integral while its peak grows? Toy model: fₙ = n on an interval of length 1/n², and 0 elsewhere. ∫|fₙ|² = 1 while ||fₙ||∞ = n. This illustrates a norm distinction, not a Navier–Stokes solution or a proof of blow-up. Explore the smooth 3D example in the graduate lesson. Full free lesson: https://www.mathwithamar.com/learn/grad-fluid-regularity-norms?utm_source=facebook&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #RealAnalysis #FluidMathematics **Instagram caption** Can a function keep the same squared integral while its peak grows? Toy model: fₙ = n on an interval of length 1/n², and 0 elsewhere. ∫|fₙ|² = 1 while ||fₙ||∞ = n. This illustrates a norm distinction, not a Navier–Stokes solution or a proof of blow-up. Explore the smooth 3D example in the graduate lesson. Try the free practice through the website link on the profile, or type mathwithamar.com/learn and search for this topic. Lesson: https://www.mathwithamar.com/learn/grad-fluid-regularity-norms?utm_source=instagram&utm_medium=organic_social&utm_campaign=academy-launch #MathWithAmar #RealAnalysis #FluidMathematics ## Review the results honestly Keep a simple sheet with date, platform, published-post URL, topic, observed views, available profile visits, observed website traffic, and adult tutoring inquiries. Record zero only when a metric is actually measured; otherwise leave it unavailable. The website dashboard does not measure local lesson-completion marks or native-app practice. Use day 7 and day 14 to choose the clearest teaching topic for a follow-up. No paid ads, follower purchases, or mass unsolicited messages are part of this kit. A useful next post answers a real mathematical question from the audience without revealing a learner’s personal details. Growth and revenue depend on use and follow-through; a two-week campaign does not guarantee income. ## Verified teaching calculations - Counting: 4 + 3 = 7, independent of spacing. - Place value: 507 = 500 + 0 + 7; 57 = 50 + 7. - Array: 4 × 7 = 7 × 4 = 28. - Fraction: 6/8 = 3/4 for the same whole. - Ratio: 2:5 = 8:20. - Road: arctan(5/100) × 180/π ≈ 2.8624°. - Sale: 80 × 0.75 × 1.08 = 64.80 under the stated tax order. - Fence: both perimeters are 40 m; areas are 84 m² and 100 m². - Budget: (100 − 36)/8 = 8 whole visits. - Tree: 20 tan(35°) + 1.6 ≈ 15.6042 m, assuming level ground. - Means: both triples have mean 10; ranges are 2 and 20. - Flow: ∫₀⁴(2 + 3t)dt = 32 L added; total 37 L. - Matrix: [[0,1,0],[0,0,2],[0,0,0]](3,4,5)ᵀ = (4,10,0)ᵀ. - Norm example: n² × (1/n²) = 1, while peak n grows. This toy function is not a Navier–Stokes solution. ## Platform guidance - [YouTube: sharing links](https://support.google.com/youtube/answer/13748639) - [TikTok: website and social profile links](https://support.tiktok.com/en/getting-started/setting-up-your-profile/linking-another-social-media-account) - [Vercel: analytics filters and tier availability](https://vercel.com/docs/analytics/filtering) Review the actual profile fields and publishing options in your account before posting.