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קשרים בין זוויות וצלעות במשולש - למורה

הנחיות למורה – עברית

משימה לתלמיד – עברית

משימה לתלמיד – بالعربية

מבנה המשימה

משימה
- מדרגה

محتوى المهمة

مهمة
- درجة

משימה

במשולש ADB נתון ש: $AD≤BD$ , $∡ADB=20°$ .

על צלע AB בנו משולש שווה צלעות ABC, כך ש:
קודקוד C נמצא בתוך משולש ADB.

מהו גודל הזווית DBC? נמקו.
מהו גודל הזווית DAC? נמקו.

מדרגה

על מנת להגיע להכללה ניתן להתחיל בבדיקת מקרים פרטיים.
ניתן להיעזר ביישומון.

יישומון למשימה

ניתן לגרור את הקודקודים $A$ , $B$ , $D$ .

יישומון למדרגה

ניתן לגרור את הקודקודים $A$ , $B$ , $D$ .

הנחיות למורה

כיתה מומלצת

כיתה ט', שליש שני.

סוג המשימה

ריבוי תשובות בטווח מסויים.

הידע הדרוש

סכום זוויות במשולש.
במשולש, מול הצלע הגדולה, מונחת הזווית הגדולה במשולש.

מה נלמד

חידוד והעמקה בקשרים בין זוויות וצלעות במשולש.

הדגשים ומטרות

הסקת מסקנות והכללה.

דירוג אתגר מתמטי

הפנייה לשימוש לבדיקת מקרים פרטיים ולשימוש ביישומון.

מערך דידקטי מומלץ

פתיחת השיעור: הצגת המשימה והנדרש בה.
עבודה עצמית של התלמידים (ביחידים, בזוגות או בקבוצות). המורה יכול לנתב את התלמידים לשימוש במדרגות, או לאפשר לתלמידים להיעזר במדרגות בהתאם לרצונם.
דיונים כיתתיים: התלמידים יציגו את הפתרונות השונים ויסיקו מסקנות בהתאם לסעיפים השונים של המשימה.

הנחיות לפתרון

$∡DBC + ∡DAC=40°$

$∡DBC≤ ∡DAC$ , לכן:

גודל $∡DAC$ בין $20°$ ל- $40°$ $(20°≤∡DAC<40°)$ .

גודל $∡DBC$ בין $0°$ ל- $20°$ $(0°<∡DBC≤20°)$ .

מפת"ח מתמטי

טלפון: 04-8288351
כתובת דוא"ל: mathkey@services.edu.haifa.ac.il
כתובת: החוג לחינוך מתמטי, הפקולטה לחינוך,
אוניברסיטת חיפה

מפת אתר

זכויות יוצרים © 2025 | כל הזכויות שמורות | תנאי שימוש באתר מפת"ח מתמטי | מרכז חמ"ה, החוג לחינוך מתמטי, הפקולטה לחינוך, אוניברסיטת חיפה, שדרות אבא חושי 199, הר הכרמל, חיפה 34988381

אין להעתיק, לצלם או לשכפל את החומרים באתר זה או קטעים ממנו בשום אמצעי.

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