Predicting a Child's Height Focus Problem Parents often wonder, usually out of sheer curiosity, how tall their child will be as an adult. When a child has a medical con are not. dition or appears to be growing abnormally, the need to under- stand his or her growth can be important. One early method involved simply doubling a child's height at age 2. This gave very inaccurate results, especially for girls. As a result, many better methods have been developed to try to accurately predict a child's eventual adult height from various factors. equivalent? Show how they are equivalent or explain why they A third method, referred to as the "mid-parent rule," uses a weighted average of the parents' heights in which the height of the opposite-gender parent is multiplied by a factor of 12/13 before it is averaged with the other parent's height. Write an formula to express this calculation. Is it equivalent to the first two formulas? Explain fully One simple method to predict adult height is to average the parents' heights and then add 2.5 inches if the child is a boy or subtract 2.5 inches if the child is a girl. This method can be fairly accurate, but can also be as much as 5 inches above or below the child's eventual height. Write one or more formulas to express this calculation, and clearly define any variables that you use These early, simple methods gave pediatricians and parents quick ways to estimate a child's adult height, but they are not terribly accurate. A new statistical model was eventually developed based on age, weight, and parental height data from a large, longitudinal study. This method, called the Khamis-Roche method, can be applied only to healthy Caucasian children over the age of 4. To use this method coefficients must be obtained from a table, multiplied by the corresponding measurement, and then added together with the constant to generate a formula to predict a child's height. The partial tables that follow give the coefficients for girls and boys aged 4 to 7. Write a formula for this method to predict the height of a 5-year-old girl, clearly defining any variables you use Another method is to add the parents' heights and then add an additional 5 inches if the child is a boy or subtract 5 inches if the child is a girl. This total is then divided by 2 to predict the child's ultimate height. Write formula or formulas for this method, using variables you've already defined. How do these formulas compare to the first ones described? Are they Coefficient of Coefficient of Coefficient of Average Current Height Current Weight Parent Height Age Constant Term 4-8.13250 55.13582 63.51039 7-2.87645 (in.) 1.24768 1.19932 1.15866 1.11342 (Ib) -0.019435 -0.017530 -0.015400 -0.013184 (in.) 0.44774 0.38467 0.34105 0.31748

Coefficient of Coefficient of Coefficient of Average Current Height Current Weight Parent Height (in.) 1.238120.0087235 1.10674 0.0064778 1.05923 |-0.0052947 1.05877 |-0.0048 144 (in.) 0.50286 0.53919 0.52513 0.48538 Age Constant Ternm (lb) 4 | -10.2567 -11.0213 6-11.1138 -10.9984 Data from: "Predicting Adult Stature Without Using Skeletal Age: The Khamis-Roche Method," Harry J. Khamis and Alex F. Roche. Use all four methods described to predict the ultimate adult height of a 5-year-old girl if her current height is 3'6" and her weight is 43 pounds. Assume her mother is 5'5" and her father is 6'1" tall. Then use all four methods again to pre- dict the height for you or someone you know. Which of these methods would have most accurately predicted the height? This focus problem is an example of a real-world challenge for which we continue to improve our response. We are much better at predicting a child's adult height now than we were decades ago. But in order to improve on a method, you need to first understand how it works. This cycle will focus on algebraic details that will help you write as well as simplify expressions and write and solve equa- tions. These skills can help you build models to do things like estimate height, as required in this problem. Understanding the details of how something works and the rules that apply is important in every discipline. This cycle will lay important foundations for the rest of your work in algebra Maybe you've seen or used an online calculator to predict height and you've wondered HOW DOES THAT How did the calculator use your data to determine an esti- mate? How much error can you expect in that estimate? Would a different calculator give you the same result? As you learn skills and concepts in this cycle, return to the focus problem and see if you have any additional insights to help you solve it. You'll see sticky notes throughout the cycle to encourage and remind you to work on the focus problem.