Let your students experiment with their graphing calculators to create a nice 4th of July display? We’ve written a brief activity that leads students with questions to manipulate parabolas, to adjust their calculator windows, and to help celebrate the Fourth. Enjoy!

# Games with dice

Time to let students become naturally curious about probability. In this activity students work in teams to record the frequency of rolled dice combinations. They observe the difference between experimental and theoretical outcomes and consider how sample size affects how close experimental and theoretical probabilities math up. Although not specifically mentioned in the activity handout, consider having the entire class combine their rolling dice data. They should see that their experimental data matches closely with actual probabilities.

# Three great World Cup activities

**World Cup ranking** - Students explore the ranking formulated from each team’s previous 4 years of play in their geographical divisions. The formula is complex and weighted. Is it fair? 5.OA, 5.NBT, 5.NF.B, 6.NS.B, 6.EE, 6.SP, 7.EE, 8.F, 8.SP, HSA

**World Cup draw** - How did FIFA sort the 32 world’s strongest soccer teams and support each geographic region? Are the first round groupings fair? 7.SP, HSS.MD, MP.1, MP.3

**World Cup – How many ways** - Students examine the rules and order of play and calculate or count how many games will be played in each group play, by all teams, and by the winning teams. 4.NBT.4, 7.G.1, 7.SP.8, MP.1

# The longest day

*Sunrise on summer solstice at Stonehenge*

On June 21st, early Saturday morning, at 6:51 am EST, the Earth’s North Pole will be tilted as far towards the Sun as it will ever be in the year. This marks the longest day of the year and the summer solstice in the Northern

hemisphere … a time that has been revered for centuries.

In this activity, students compare length of daylight to place latitude while studying the correlation, evaluating Excel generated formulas, and appreciating the significance of this date.

# World Cup – How many ways?

How many games are played in each round of the World Cup? In the opening round each of the four teams in a group must play each other (round robin format). From then on each round is a knock-out round … if you lose then you are out. Let your students enjoy learning about what they are watching and question what and how much each team must do. There is so much math in the World Cup games. Enjoy!

# World Cup draw

This is part II of our reflections on the World Cup games. Part I, World Cup rankings, explained and let students practice with the formula and weighting that is used to establish each country’s team rank.

This second activity deals with the method of sorting the teams into 4-team groups for the first round of play. Students can study the draw, make observations, and then try to create what they think might be a more fair method for deciding which countries should compete in the opening matches.