## Posts Tagged ‘Middle school’

## Have Yourself a Mathsy Little Christmas

December 5, 2019## It is Xmas … Ah! The Joy of Algebra!

December 5, 2019**Great Math Xmas Ornament Ideas for Middle School here @ MathEqualsLove blog.**

**Mathematicians can make mountains out of mince pies, but in this case Dr Eugenia Cheng, who is Professor of Pure Mathematics at the University of Sheffield, UK, makes it look fun. The video clip includes some great Middle School Maths that you can eat.**

## Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . METRIC UNITS

November 13, 2019

With the catastrophic Californian fires burning into November and wildfires currently burning in NSW and Qld, Australia, I had to repost this firefighter maths for middle school classrooms.

Radiant Heat Stats WA Fire **Dept FACEBOOK**, Australian Bushfires 14 NOV 2019 **MyFireWatch WA**

Wildfires USA 2019 Map: **Ecowest,**

# METRIC UNITS

**Background Story**

On **5 ^{th} August 1949 Wag Dodge** was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.

# HOW FAST CAN YOU RUN?

# METRIC UNITS

## Time Trial:

Mark out a 10 m course. Make 3 time trials.

t_{1 }=

t_{2} =

t_{3}=

Average your time:

t_{av} = (t_{1 } + t_{2} + t_{3)}/ 3 =

Your Speed S = 10/t_{av} = ……… m/sec

## HOW FAST IS A GRASS FIRE?

This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at **20kph** (up to 30 kph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 20 kph = 20 x1000/(60 x 60)

= 20 x 0.27777777 = 20 x 0.28 m/sec

= 5.6 m/sec

# CAN YOU OUT RUN A FIRE?

__Average Running Speed Boy__ 13–14 yo = 3.0 m/sec

__Average Running Speed Girl__ 13–14 yo = 2.4 m/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 3.0 m/sec. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

This is not looking good. See more Firefighters Need Maths **here**.

We can do very accurate calculations using simultaneous equations.** Wildfire Algebra**: Detailed Worksheet using simultaneous equations and solutions **here**.

# NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?

We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.

Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:

Each 10º increase in slope, the **fire front speed doubles**.

Now you can calculate the distance travelled by the fire front up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator **here**.

Even at your top running speed, which is unlikely up a slope, you can run 180 m in 1 minute. In that time the forefront has moved 2688 m or 2.7 km.

It depends how far away you are from the fire front, but it seems you cannot out run this fire front.

Again we can do very accurate calculations using simultaneous equations.

See Firefighters Need Maths **here**.

Wildfire Algebra: Worksheet and solutions **here**.

# CAN YOU OUT RUN A WILD FIRE?

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 110 kph and temperatures up to 2000 °C, which can and does melt glass and cars.

The fire front speed doubles with every 10º, so speeds for the fire front can reach 220 kph, 330kph and up to 550kph.

# What happened to the Smoke Jumpers?

When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?

ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.

## Amazing and Terrifying Wildfire Maths . . . . . . . . . . . . . . USA UNITS

November 13, 2019With the catastrophic Californian fires burning into November and wildfires currently burning in NSW and Qld, Australia, I had to repost this firefighter maths for middle school classrooms.

Radiant Heat Stats WA Fire **Dept FACEBOOK**, Australian Bushfires 14 NOV 2019 **MyFireWatch WA**

Wildfires USA 2019 Map: **Ecowest,**

# USA UNITS

**Background Story**

On **5 ^{th} August 1949 Wag Dodge** was dropped by parachute with 14 other fire fighters into Mann Gulch, a steep-sided gully in a Montana pine forest. Fire fighters who parachute in to put out small blazes started by lightening are called Smoke Jumpers. As they worked their way down the sides of the gully the breeze was blowing away from them. But the wind soon shifted. This produced an updraft, which increases the speed of the fire front. The 15 Smoke Jumpers turned and started running for their lives uphill.

# HOW FAST CAN YOU RUN?

# USA UNITS

## Time Trial:

Mark out a 30ft course. Make 3 time trials.

t_{1 }=

t_{2} =

t_{3}=

Average your time:

t_{av} = (t_{1 } + t_{2} + t_{3)}/ 3 =

Your Speed S = 30/t_{av} ft/sec

# HOW FAST IS A GRASS FIRE?

This will, of course, vary depending on the wind speed. A typical grass fire in Australia in a flat area can travel at **12mph** (up to 20mph) in a gentle breeze.

Fire Front Speed Grass Fire

Fire Front Speed = 12 mph = 12 x 5280/(60 x 60)

= 17.6 ft/sec

= 18 ft/sec

# CAN YOU OUT RUN A FIRE?

__Average Running Speed Boy__ 13–14 yo = 10 ft/sec

__Average Running Speed Girl__ 13–14 yo = 8 ft/sec

We’ll assume, boy or girl, that you are really motivated and can run away from the fire at top speed of 10 ft/sec and -Wow! – this is easy math. Now calculate the distance you can run and the fire front moves in 10 secs intervals up to 1 minute.

This is not looking good. See more Firefighters Need Maths **here**.

We can do very accurate calculations using simultaneous equations.** Wildfire Algebra**: Detailed Worksheet using simultaneous equations and solutions **here**.

# NOW YOU ARE RUNNING UP HILL. WHAT HAPPENS?

We’ll assume, due to being motivated by having a fire licking your heels, that you can run at your top speed up hill for a short time, at least. But here is the problem.

Heat rises and so there is a Chimney Effect pushing the fire uphill. The rule of thumb used by fire fighters is:

Each 10º increase in slope, the **fire front speed** doubles.

Now you can calculate the distance travelled up a slope at a 30º angle.

Don’t forget you can use the WEB 2.0 Calculator **here**

Even at your top running speed, which is unlikely up a slope, you can run 1080 ft in 1 minute. In that time the forefront has moved 8640 ft or 1.6 miles. It depends how far away you are from the fire front when you start running, but it seems likely that you cannot out run this fire front.

Again we can do very accurate calculations using simultaneous equations.

See Firefighters Need Maths **here**.

Wildfire Algebra Worksheet and solutions **here**.

# CAN YOU OUT RUN A WILD FIRE?

High winds can turn a bush or forrest fire into a WILD FIRE with wind speeds up to 70 mph and temperatures up to 2000 °C, which can and does melt glass and cars.

The fire front speed doubles with every 10º, so speeds for the fire front in a strong wind can reach 140 mph, 210 mph and up to 280 mph.

# What happened to the Smoke Jumpers?

When the fire front changed direction Wag Dodge and 14 other Smoke Jumpers found themselves running for their lives up a steep slope. What did Wag do next?

ANS: Here’s the amazing thing. Wag realised he could not out run the fire at that point. So he stopped. Took off his back pack. Took out some MATCHES and lit a fire in the grassy patch in front of him. Just before the firewall hit he threw himself face down on the burnt patch. He survived. The other 14 firefighters did not.

## Why do so many students HATE MATH? … um, you know, BOREDOM

September 28, 2019According to **‘Bored Out of Their Minds’,** an article by ZACHARY JASON in The Harvard Ed Magazine (2017):

**Boredom accounts for nearly a third of the variation in student achievement. **

**Half of high school dropouts cite boredom as their primary motivator for leaving.**

Boredom begins for Math students at Grade 6 when students (Common Core Standards, USA) tackle more abstract concepts such as linear eqns, exponents, probability, geometry and so on.

Math curriculums in the USA, UK & Australia all demand students solve REAL LIFE problems. Too often these are of the type:

Q. Ronaldo has tethered his goat on a 12ft rein in the corner of a 20ft square field. What area can the goat graze?

**THE ANS: Who cares?**

# Simple.

# Ask students maths questions which have answers they want to know.

Students really don’t care about Ronaldo’s goat, but here are some questions which involve intriguing answers they might want to work out. And many of these questions involve funny or age-relevant activities, which also helps engagement.

**1. Mean, Median STATS:** **Mean, Median and Coffee: Busting an Urban Myth**

**2. Parabolas: ****Can you beat the 12-14 yo World Record for a Watermelon Pip spit?**

**3. Geometry:** **Build a Freestanding Tower**

**Rates (Speed) & Units:**

**4a.** **The Terrifying Math of Running from a bear**

**5. Decimals, %, Volume:** **What Volume of alcohol is lethal for teens?**

**6. Decimals, Algebra, Weight Units**

**How much blood can a kid lose and survive?**

Graph **Hunger Game Math**

**7. GEOMETRY. Angles**

**Any Topic:**

**8.** **Middle School Math Photo Scavenger Hunt**

Space Math Song** here**

**EVEN TEACHERS GET BORED!!!**

The average time it takes **an audience at a conference** to switch off is 11 minutes. Keep in mind this audience is, at least, being paid to be bored witless.

## Outdoor Math Adventures___________ Middle School

September 9, 2019As the weather improves – Spring in Melbourne, my city & Autumn in USA & UK – it is an ideal time to take math outdoors. Here are some fab exercises for Middle School Math.

**Lego Man soccer fields will vary in size depending on the height of each player picked by each student. This does your head in. It is really challenging maths!**

**McGill Uni link here.**

Don’t forget to throw in Mathspig’s lame protractor jokes.

**You’ll find full calculations at the Maths is Fun blog.**

**You’ll find more fab outdoor junior and middle school maths activities at the terrific Maths and Movement blog.**

**Some students will discover their co-ordinate point is not on the grid. Students should then work out that they will need a different scale for the y-axis. You can get more inspiration at the Stand Again blog.**

## Make a Cool Pattern with x2 Tables… but it is trickier than you think.

September 6, 2019## A COOL MIDDLE SCHOOL MATH EXERCISE

This idea comes from Burkard and Giuseppe @ the fabulous MATHOLOGER channel. Students can make a pattern called a cardioid that pops up all over math according to Burkard.

Follow these steps. There is a pdf file below the first diagram for printing exercise sheets.

And then watch the MATHOLOGER video for a really interesting explanation.

**x2 Tables on a Circle pdf file for printing**

**This circle graph blank could also be used for x3 and x4 tables, ****which produce totally different yet equally amazing patterns.**

Halfway there, now it gets tricky. +52 to each point on the circle and keep multiplying by 2.

ie. 27 x 2 = 54, 28 x 2 = 56 and so on.

so 0 = 52, 1 = 53, 2 = 54, 3 = 55, 4 = 56 etc

This shape is called a CARTIOID.